hydraulic stability of cubipod armour units in breaking conditions

Hydraulic stability of Cubipod armour units in Breaking conditions

Lien Vanhoutte

Promotor: Prof. Josep Medina (UPV Valencia) Co-Promotor: . Prof. dr. ir. Julien De Rouck Masterthesis to obtain the degree: Master of Science in Civil Engineering Laboratory of Ports and Coasts, Polytechnic University of Valencia Departement of Civil Engineering, Ghent University Academic year 2008-1009

i

Preface

I would like to thank my tutor of this project Prof. Medina for giving me the great opportu-

nity to make my �nal year project at the Laboratory for Ports and Coasts of the Polytechnic

University of Valencia, and for his guidance throughout the project.

Special thanks also to Prof. De Rouck as my Erasmus-coordinator and co-tutor of this thesis

for providing the possibility of this abroad experience.

Deep gratitude goes to Guille, for his guidance throughout the project, for sharing his ex-

perience, for helping me with every single doubt, for encouraging me and helping me out in

the stressful moments. A warm thanks as well to Jorge, Vicente, Kike, Mireille, Steven, César

and Pepe, for providing a very nice working space in the laboratory.

Finally I want to thank my parents, my sisters, friends, and �at mates in particular, for

their support and many hours of listening during this thesis.

COPYRIGHTS

The author grants the permission for making this thesis available for consultation and for

copying parts of this thesis for personal use.

Any other use is subject to the limitations of the copyright, speci�cally with regards to the

obligation of referencing explicitly to this thesis when quoting obtained results.

1st of June 2009,

Lien Vanhoutte

ii

Overview

Hydraulic stability of Cubipod armour units in

breaking conditions

Author: Lien Vanhoutte

Master thesis to obtain the degree of Master of Civil Engineering

Academic year 2008-2009

Tutors:

Prof. Josep R. Medina, Laboratory of Ports and Coasts, Polytechnic University of Valencia

Prof. Julien De Rouck, Department of Civil Engineering, Ghent University

Summary

In this report, the study of the new armour unit, Cubipod, designed by the Laboratory of

Ports and Coastas of the Politecnic University of Valencia, is described. The general stability

of mound breakwaters are discussed and an overview of di�erent existing armour elements is

given. Further, the wave height distribution in shallow water is analysed theoretically and

compared with the obtained results. An experimental study of the Cubipod armour unit is

carried out on a physical scaled mound breakwater model in breaking conditions. Results on

re�ection and damage progression are presented and compared with previous similar tests in

deepwater conditions. A �rst estimation of the hydraulic stability coe�cient of the Cubipod

in breaking conditions is proposed. The results show that the Cubipod has low re�ection and

high hydraulic stability.

Keywords: Cubipod - armour unit - mound breakwater - hydraulic stability - breaking

conditions

HYDRAULIC STABILITY OF CUBIPOD ARMOURUNITS IN BREAKING CONDITIONS

L. Vanhoutte1

Supervisor(s): J.R. Medina2, J. De Rouck3

1 Masterthesis student, Faculty of Engineering, Ghent University, Belgium2 Professor, Lab. of Ports and Coasts, Polytechnic University of Valencia, Spain

3 Professor, Faculty of Engineering, Ghent University, Belgium

Abstract—In this Masterthesis an experimental study of the Cubipod ar-mour unit was carried out on a physical model breakwater in shallow water.The Cubipod is a new armour unit, designed by the Laboratory of Ports andCoasts of the Universidad Politcnica de Valencia. As the wave height is animportant value when designing mound breakwaters, theories estimatingthe maximum wave height in breaking conditions were studied and com-pared with the measured results in the Laboratory. Results on reflectionand damage progression were presented and compared with previous sim-ilar tests in deepwater conditions. An estimation of the hydraulic stabilityKD coefficient of the Cubipod in breaking conditions was proposed usingthe Virtual Net Method[2]. The results show that the Cubipod has low re-flection and a high hydraulic stability.

Keywords—Cubipod - armour unit - mound breakwater - hydraulic sta-bility - breaking conditions

I. INTRODUCTION

Mound breakwaters play an important role in the protectionof harbours. They have many failure modes, but the most im-portant one is the loss of hydraulic stability of the armour layerunder wave attack. This can be caused by direct extraction ofarmour units, or by excessive settlement causing HeterogeneousPacking of the armour layer as described by Gomez-Marton &Medina [2].

Generally, mound breakwaters are placed in shallow waterand thus subjected to breaking conditions. An important fac-tor influencing the hydraulic stability is the maximum incidentwave height. Hydraulic stability of armour layers has been in-tensively studied in literature and several formulae have beenproposed for predicting armour damage. The first models wereonly valid for stationary conditions. In 1988, Van der Meer [8]proposed a first formula for irregular waves. Medina [7] pro-posed a method applicable to nonstationary conditions, basedon an exponential model for individual waves of the storm. Themost frequently cited armour stability formula was published byHudson in 1959[4] for regular waves, and later popularized forirregular waves by SPM using the equivalences H1/3 and H1/10

as representative of the wave height.

II. ARMOUR UNITS

Originally, harbours were built with wooden or stone con-structions. The continuous growing of the harbours meant aneed for higher stones and design of artificial concrete armourunits was forced. Many different breakwater armour units ex-ist, each with their own advantages and disadvantages. Theircharacteristics have an important influence on the hydraulic sta-bility of the mound breakwater and explains why improvementand development of armour units is still an important subject ofresearch.

The Cubipod armour unit is designed to benefit from the ad-vantages of the traditional cube, but to correct the drawbacks.Therefore, the design of the unit is based on the cube in order toobtain his robustness. The protuberances of the Cubipod avoidface-to-face settlement and increase the friction with the filterlayer as can be seen in figure 1. They avoid sliding of the ar-mour elements and thus, Heterogeneous Packing and loss of el-ements above the still water level is reduced. All this indicates ahigher hydraulic stability of Cubipods in comparison with cubeelements, which was proved in earlier executed tests [3].

Fig. 1. The new armour unit: the Cubipod

III. EXPERIMENTS

Regular experiments on five different physical model break-waters were carried out in the 2D wave flume of the laboratoryof Ports and Coasts in the Polytechnic University of Valencia. Asection with a double layer of Cubipods, one with a single layerof Cubipods, each with and without toe berm were considered.Finally, experiments were carried out on a section consisting ofa cube layer covered by a Cubipod layer.

The unit weight of the Cubipods is 128g, and they have adensity of 2300kg/m3. The water depth changes from 30cm to42 cm near the model. For every water depth different periodswere considered, lancing waves with increasing wave height forevery period. The wave height was increased until breaking oc-cured. Registered wave heights were separated in incident andreflected waves with the LASA V-method (Figueres & Medina[1]), and the reflection coefficient was obtained as CR [%] =Hr/Hi. Damage progression was analysed visually, establish-ing the damage levels Initiation of Damage, Iribarren Damageand Destruction, as well as quantitatively, using the Virtual NetMethod proposed by Gmez-Martn & Medina [2], which allowsto measure also the failure mode of Heterogeneous Packing, andnot only extraction of armour units.

IV. RESULTS

A. Breaking wave height

The incident wave height is an important factor influencingthe design of coastal structures. An overly conservative estima-tion of this value can greatly increase costs and make projectsuneconomical, whereas underestimation could result in struc-tural failure or significant maintenance costs. A short study con-cerning the maximum wave height in breaking conditions wasexecuted.

Different theories exist to estimate this maximum value.Many theories however, overestimate this value. Further, theysuppose mostly that the energy from the broken waves is con-centrated in the breaking wave height, which means that all thebroken waves have the breaking wave height in the surfing zone.This statement however didn’t correspond with the reality. Theenergy from the broken waves was distributed back over thesmaller wave heights in the distribution. In Fig. 2 is the theoryof Le Roux (2007) [6] shown to estimate the real wave heights.The estimation is similar to the measured values, however, heunderestimates the breaking wave height and supposes a con-stant wave height after breaking, independent of the wave pe-riod.

Fig. 2. Graphic showing the theory of Le Roux (2007) [5] to estimate the waveheight, compared with the measured results in the Laboratory

B. Hydraulic stability

The reflection coefficient differs between 10% and 30% forkh > 1, 5 and increases until 50% for small kh values. For highkh values, the type of armour layer has a big influence on thereflection coefficient and a single layer reflects less energy thana double layer. For small values of kh, however this influencedecreases and becomes nil. Reflections coefficients in shallowwater is lower than in deepwater conditions because the crestbreaks and a lot of energy is dissipated which means less reflec-tion.

Damage analysis resulted in a higher hydraulic stability forsections with toe berm, because there is no increase of porosityat the bottom of the breakwater. Those are the common builtbreakwater sections. Hydraulic stability coefficients of KD=28

for a double layer of Cubipods with toe berm and KD=23 fora single layer were found. KD=18 was found for a combinedarmour layer with cubes and Cubipods. Comparison betweenthe damage progression in deepwater conditions and in shallowwater shows us that KD in shallow water is less than in deepwa-ter conditions. Waves with higher energy reach the breakwater,which means that the damage will initiate earlier than in deep-water conditions. In Fig. 3, the damage progression for the dif-ferent breakwater sections are shown, with D0,2 the linearizeddimensionless damage proposed by Medina [6] and indicationof the Initiation of damage and Initiation of Iribarren damage.

Fig. 3. Linearised dimensionless equivalent damage as a function of dimension-less wave height for the different studied breakwater sections

V. CONCLUSION

Calculating a mound breakwater in breaking conditions, spe-cial attention has to paid to the maximum wave height. Manyexisting theories overestimate this wave height, which can re-sult in uneconomical results. According to the executed tests,the Cubipod proves to have a high hydraulic stability in break-ing conditions and shows to be a very promising armour unit,with a simple and robust shape, an easy placement pattern and ahigh hydraulic stability compared with other armour units, alsoin breaking conditions.

VI. BIBLIOGRAPHY

(1) Figueres, M. & Medina, J.R.: Estimation of incident and reflected wavesusing a fully nonlinear wave model. Proc. of the 29th Coast. Eng. Conf., pp.594-603, 2004.(2) Gomez-Martin, M.E. & Medina, J.R.: Analisis de averas de diques en taludcon manto principal formado por bloques de hormigon. VIII Jorn. Espaolas deIng. de Costas y Puertos, 2005.(3) Gomez-Martin, M.E. & Medina, J.R.: Cubipod concrete armour unit andHeterogeneous Packing. Proc of Coast. Structures, ASCE, 2007.(4) Hudson: Laboratory investigation of rubble mound breakwaters. J. Wtrwy.,Port, Coast. and Oc. Division, 85(3):93-121, 1959.(5) Le Roux, L.: A simple method to determine breaker height and depth fordifferent deepwater height/length ratios and sea floor slopes. Coastal Engr. 54,271-277, 2007.(6) Medina, J.R., Hudspeth, R.T. and Fassardi, C.: Breakwater armor damagedue to wave groups. J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 120(2),pp.179-198, 1994.(7) Medina, J.R.: Wave climate simulation and breakwater stability. Proc. of the25th Coast. Eng. Conf., ASCE, pp. 1789-1802, 1996.(8) Van der Meer, J.W.: Suitable wave-height parameter for characterizingbreakwater stability. J. of Waterw., Port, Coast. and Oc. Eng., ASCE, 114(1):66-80, 1988.

Contents

Extended abstract ii

List of Figures ix

List of Tables xiii

1 Introduction 1

2 Stability of Mound Breakwaters 4

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 A Short History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Analysis of the stability of a mound breakwater . . . . . . . . . . . . . . . . . . 9

2.3.1 General stability of a mound breakwater . . . . . . . . . . . . . . . . . . 9

2.3.2 Heterogeneous packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2.2 Heterogeneous packing . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.3 Damage criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Quantization of the stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.1 Formula to calculate the stability of a mound breakwater . . . . . . . . 16

v

Contents vi

3 Armour Units 18

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 History: the armour units since the 50's . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Classi�cation of armour units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 A new armour unit: The Cubipod . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.2 Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4.3 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Wave height in breaking conditions 33

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 The surf zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Types of breaking waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.4 Models to estimate the wave height distribution . . . . . . . . . . . . . . . . . . 36

4.5 Maximum wave height in breaking conditions . . . . . . . . . . . . . . . . . . . 38

5 Experimental setup 43

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 The Test Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2.1 2D Wave Flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.2 Wave Generation System . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.3 Wave Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2.4 Energy dissipation system . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2.5 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.3 Calibration of the wave �ume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.4 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Contents vii

5.4.1 Physical characteristics of the studied model . . . . . . . . . . . . . . . . 50

5.4.2 Construction of the physical model . . . . . . . . . . . . . . . . . . . . . 54

5.4.2.1 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.4.2.2 Control of the material characteristics . . . . . . . . . . . . . . 56

5.4.2.3 Construction of the model . . . . . . . . . . . . . . . . . . . . . 59

5.4.2.4 Reconstruction of the model . . . . . . . . . . . . . . . . . . . 61

5.4.2.5 Placement of the sensors . . . . . . . . . . . . . . . . . . . . . 63

5.4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.3.1 Realized experiments . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.3.2 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . 65

5.4.4 Procedure to analyse the data . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4.4.1 Separating the incident and re�ected waves: LASA V . . . . . 66

5.4.4.2 Analysis of the waves: LPCLAB 1.0. . . . . . . . . . . . . . . . 67

5.4.4.3 Analysis of the re�ection coe�cient . . . . . . . . . . . . . . . 69

5.4.4.4 Analysis of the damage progression . . . . . . . . . . . . . . . . 70

6 Results 77

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2 Calibration of the wave �ume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3 Interpretation of the theories calculating the maximum wave height . . . . . . . 80

6.4 Hydraulic stability of the mound breakwater . . . . . . . . . . . . . . . . . . . . 85

6.4.1 Wave re�ection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.4.1.1 The re�ection coe�cient in function of kh . . . . . . . . . . . . 85

6.4.1.2 The re�ection coe�cient in function of Ir . . . . . . . . . . . . 87

6.4.1.3 Comparing with the re�ection coe�cient in deepwater . . . . . 88

Contents viii

6.4.2 Damage analysis on the armour layer . . . . . . . . . . . . . . . . . . . . 93

6.4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.4.2.2 Qualitative analysis . . . . . . . . . . . . . . . . . . . . . . . . 93

6.4.2.3 Quantitative analysis . . . . . . . . . . . . . . . . . . . . . . . 96

7 Conclusions 102

A Terminology of the experiments 104

B Wave �ume 106

C Working of the AWACS 108

D Seperation of incident and re�ected waves 113

E Calculation of the initial porosity 115

F Example of a test report 116

G Test results 119

Bibliography 130

List of Figures

2.1 Mound Breakwater failure modes de�ned by Bruun . . . . . . . . . . . . . . . . 10

2.2 The two most important failure modes by mound breakwaters: extraction of

armour elements and heterogeneous packing. The classical view vs. the hetero-

geneous packing view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Face to face �tting by cubes reducing the friction with the �lter layer . . . . . . 19

3.2 A selection of the existing concrete armour units . . . . . . . . . . . . . . . . . 23

3.3 A new armour element: the Cubipod . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Drop test results of Cubipods compared with cubes showing the lost weight . . 30

3.5 Penetration of the Cubipods in the armour layer . . . . . . . . . . . . . . . . . 30

3.6 The separating e�ect of the protuberances avoiding the face-to-face arrangement 31

3.7 Example of placement in a depository of Cubipods . . . . . . . . . . . . . . . . 32

3.8 The casting system designed by SATO and the tongs for movement and man-

ufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 Types of breaking waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Distribution of the wave heights by breaking, concerning that all the broken

wave heights will have the breaking wave height in the sur�ng zone . . . . . . . 37

4.3 Distribution of the breaking wave heights over the distribution of the unbroken

waves (Goda [46]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

ix

List of Figures x

5.1 Longitudinal section of the 2D wave-�ume . . . . . . . . . . . . . . . . . . . . . 44

5.2 Wave generation system in the LPC wave �ume and setup of active wave ab-

sorption system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3 Wave gauges for wave measurement and Step-Gauge Run-up Measurement Sys-

tem (S-GRMS) constructed by University of Ghent . . . . . . . . . . . . . . . . 48

5.4 Wave energy dissipation system in the LPC wave �ume . . . . . . . . . . . . . . 49

5.5 Cross section of the studied models: 2 layers of Cubipods (C2), 1 layer of

Cubipods (C1), 1 layer of cubes covered by one layer of Cubipods (CB) . . . . 52

5.6 Cross section of the studied models: 2 layers of Cubipods with toe berm (C2B),

1 layer of Cubipods with toe berm (C1B) . . . . . . . . . . . . . . . . . . . . . 53

5.7 Draw the cross section of the mound breakwater on the wall of the canal . . . . 55

5.8 The concrete grout to provide a rough surface for the model . . . . . . . . . . . 55

5.9 Grading curve for the core material . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.10 Grading curve for the �lter material . . . . . . . . . . . . . . . . . . . . . . . . 58

5.11 Construction of the model: the core and the �lter . . . . . . . . . . . . . . . . . 59

5.12 Construction proses of the armour layer . . . . . . . . . . . . . . . . . . . . . . 62

5.13 Construction of the �lter on the inner slope and a crest on the top of the mound

breakwater after destruction of the core and the �lter layer . . . . . . . . . . . 63

5.14 Parameter window of the LASA-V software . . . . . . . . . . . . . . . . . . . . 67

5.15 Example of the separation of incident and re�ected wave trains by LASA V . . 68

5.16 Parameter window of the LPCLab software . . . . . . . . . . . . . . . . . . . . 69

5.17 Virtual net to measure the equivalent damage analysis and counting the units

in AutoCAD for damage calculation . . . . . . . . . . . . . . . . . . . . . . . . 73

5.18 Above: foto with the real net and the designed net in Photoshop (start of the

tests with h=38). Under: foto without the real net and the pasted virtual net

in Photoshop (end of the tests with h=38) . . . . . . . . . . . . . . . . . . . . . 74

5.19 Damage levels in the armour layer . . . . . . . . . . . . . . . . . . . . . . . . . 76

List of Figures xi

6.1 Results of the calibration of the wave �ume . . . . . . . . . . . . . . . . . . . . 79

6.2 Theoretical models to estimate the breaking wave height in function of the

water depth, compared with the maximum measured wave height: Keulegan

and Patterson (K&P), Collins for di�erent slopes, SPM for di�erent slopes and

Weggel for a horizontal bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.3 Theoretical models to estimate the relation Hb/H0 in function of H0/L0, com-

pared with the measured results: Komar and Gaughan (K&G), Sakai and Bat-

tjes (S&B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.4 Theorecal model of Le Roux to estimate the real water wave height for h=30cm,

compared with the measured results . . . . . . . . . . . . . . . . . . . . . . . . 84

6.5 The re�ection coe�cient (CR) in function of the dimensionless relative wave

depth (kh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.6 The re�ection coe�cient in function of the dimensionless relative water depth

(kh): comparing single and double layers of Cubipods . . . . . . . . . . . . . . 90

6.7 The re�ection coe�cient in function of the dimensionless relative water depth

(kh): comparing a combined cube-cubipod layer with a double layer of Cubipods

and a single layer of Cubipods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.8 The re�ection coe�cient (CR) in function of the number of Iribarren . . . . . . 92

6.9 In�uence of the presence of a toe berm on the hydraulic stability of a mound

breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.10 The linearised dimensionless damage as a function of a dimensionless height.

Above: the qualitative calculated KD's. Under: the quantitative calculated KD 100

6.11 Comparison a double Cubipod layer in breaking with non-breaking conditions,

and with Quarrystone in breaking conditions. Dimensionless damage as a func-

tion of dimensionless wave height . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.1 Cross section of the 2D wave-�ume of the Laboratory of Ports and Coasts of

the Politecnic University of Valencia . . . . . . . . . . . . . . . . . . . . . . . . 107

C.1 A detailed scheme of the working of the AWACS . . . . . . . . . . . . . . . . . 110

List of Figures xii

C.2 The steps to activate the control system . . . . . . . . . . . . . . . . . . . . . . 110

C.3 Software to manage the AWACS. Above: the startscreen Under: the calibration

of the AWACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

C.4 Windows to realize the wave generation . . . . . . . . . . . . . . . . . . . . . . 112

C.5 The program Multicard, for the aquisition of the datas . . . . . . . . . . . . . . 112

E.1 Calculation of the initial porosity . . . . . . . . . . . . . . . . . . . . . . . . . . 115

F.1 Example of a test report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

F.2 Example of a test report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

List of Tables

2.1 Hydraulic stability criteria for the armour layer of a mound breakwater as cited

in[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Classi�cation of breakwater armour units by shape [34] . . . . . . . . . . . . . . 24

3.2 Classi�cation of armour units by shape, placement and stability factor. . . . . . 26

3.3 Classi�cation of armour units by placement method and structural strength

(Mijlemans, 2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Type of breaking in function of the number of Iribarren . . . . . . . . . . . . . 35

5.1 Calculating the theoretic equivalent cube size and the theoretic volume of the

Cubipods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2 Theoretic characteristics of the used materials . . . . . . . . . . . . . . . . . . . 51

5.3 Grading characteristics of the core material . . . . . . . . . . . . . . . . . . . . 57

5.4 Grading characteristics of the �lter material . . . . . . . . . . . . . . . . . . . . 58

5.5 Theoretical and measured characteristics of the Cubipods . . . . . . . . . . . . 59

5.6 The real initial porosity in the di�erent models [%] . . . . . . . . . . . . . . . . 61

5.7 Position of the wave gauges and distance between them in the canal . . . . . . 64

6.1 Incident wave heights producing the levels of damage: IDa and IIDa . . . . . . 94

xiii

Chapter 1

Introduction

Breakwaters are arti�cial structures with the principal function of protecting a coastal area

from excessive wave action, as there are ports, port facilities, coastal areas and coastal instal-

lations. They reduce the transmitted energy by forcing the waves to break and re�ect when

hitting the breakwater.

Very often, an original harbour is protected in a natural area. As the economy keeps growing,

the importance and application of the ports increase and a continuous port expansion is

necessary. Growing ship draughts also oblige to expand the existing ports. Due to this facts,

the natural protection can no longer resist the wave action and ports grow through sea side.

Breakwaters start to play an important role.

Generally, breakwaters are divided in two di�erent types: mound breakwaters and vertical

breakwaters. The mound breakwaters are sloped structures, constructed with a low permeable

core, covered by one or two �lter layers and an armour layer. The dissipation of wave energy

is mainly through absorbtion, but also re�ection plays an important role. A principal design

objective is to determine the size and layout of the components of the cross-section. Designing

and constructing a stable structure with acceptable energy absorbing characteristics continues

to rely heavily on past experience and physical modelling. Vertical breakwaters function

mainly in re�ecting the incident waves and consist of a vertical wall, resting on a rubble

mound foundation.

1

Introduction 2

In the beginning of the mound breakwater use, they consisted typically of quarrystone, sta-

bilised by their own weight. As ports kept growing, the mound breakwaters had to resist higher

wave action. This was no longer possible with quarrystone, as their size is limited. Concrete

units were used. First, the elements were simple cubes, but soon, problems concerning those

elements were discovered. Later on, di�erent shapes were developed, each with their own

advantages and disadvantages. They di�er in placement pattern, risk of progressive failure,

number of layers, structural strength and hydraulic stability. Failures in the 70's, however,

showed that slender units, designed for maximum interlocking, provide insu�cient structural

stability, which may cause progressive failure. This event set an end to the rapid development

of elements with high hydraulic stability and reduced weight. The 80's meant a decade of big

changes: not only the hydraulic stability and interlocking, but also the structural strength

and robustness of the elements has been recognized.

The aim of this project is to study the characteristics of the Cubipod in breaking conditions.

The Cubipod is a new armour element, invented by the Laboratory of Ports and Coasts in the

Polytecnic University of Valencia. In recent history, stability studies in deepwater conditions

showed successful results for this element and also overtopping performance seemed to be

smaller in comparison with cubes. Now, an experimental study of the hydraulic stability of

the Cubipod armour unit has been carried out on a physical scale model in 2D, in shallow

water. Di�erent models are obtained: a model with a double armour layer, with a single

armour layer and with a combined layer of cubes covered by a Cubipod layer. The main

objective is determining the hydraulic stability in breaking conditions and to compare those

results for the di�erent sections. The results also will be compared with the earlier obtained

results in the deepwater tests.

In Chapter 2, as theoretical background on breakwater design, the stability of a mound break-

water is discussed. First a historical resume is given, starting by the �rst published formula

to calculate the weight of rock materials of a mound breakwaters until the last developments.

This is followed by an overview of the di�erent failure modes and the quantization of the

stability.

Chapter 3 provides an overview of the di�erent existing armour units. A historical overview

Introduction 3

since the 50's is given, followed by di�erent systems to classify the existing armour units.

Further, the new armour unit, the Cubipod, is presented, given its idea and concept including

the di�erent advantages of the element.

In Chapter 4, the maximum existing wave height in shallow waters is brie�y discussed. Di�er-

ent types of wave breaking are mentioned and models to estimate the wave height distribution

are discussed followed by theories to estimate the maximum wave height in breaking condi-

tions.

In Chapter 5, the experimental setup is described, including the test equipment and the

experimental design. Here the physical characteristics of the studied model are given, the

construction of the model is described and the experimental procedure and the entire procedure

to analyse the data are given.

Chapter 6 gives the results of the realised tests. The theories estimating the maximum wave

height in breaking conditions are compared with the measured results in the Laboratory. The

re�ection results, damage progression and estimation of the hydraulic stability coe�cient KD

for the di�erent sections are discussed. Those results are compared to previously executed

test in deepwater conditions.

Finally, Chapter 7, presents the conclusions of the realized work.

Chapter 2

Stability of Mound Breakwaters

2.1 Introduction

Mound breakwaters are the most commonly used breakwaters in Europe because of their easy

construction and reparation process, high capacity to disperse the incoming energy and resist

big storms. Design of mound breakwaters, however is a complex theme and has been studied

across the world. An important evolution is made from elementary studies, considering only

stationary regular waves to more complicated models, able to predict breakwater stability due

to non-linear wave action in non-stationary conditions.

The most important parts of a traditional mound breakwater are the core, �lter layers, the

armour layer, the toe and the crest. The bulk of the cross-section comprises a relatively

dense rock �ll core, forming the base of the mound breakwater. This core should form a good

foundation for the �lter layers which avoid the small particles of the core to escape and has to

be relative impermeable to avoid transmission of energy through the mound breakwater. The

armour layer, founded on the �lter layer(s) consists of rock or concrete blocks and should be

permeable and robust to protect the mound breakwater against excessive wave action. The

dissipation of wave energy occurs rather through absorption than re�ection. Incident wave

energy is dissipated primarily through turbulent run-up within and over the armour layer.

If the wave is steep or the seaward slope of the breakwater is relatively �at then the wave

will overturn and plunge onto the slope, dissipating further energy. Sometimes a screen wall

4

Stability of Mound Breakwaters 5

is placed above the crest of the mound breakwater to avoid overtopping and improve the

conditions during construction.

In this chapter, a brief historical background concerning the most important evolutions in

the studies of mound breakwaters is given. Further a study of the analysis of their stability

is described, including the description of a new failure mode called heterogeneous packing,

followed by the way to quantify the stability of an armour layer.

2.2 A Short History

Breakwater design depends on many variables as there are: wave height, water density, armour

density, armour slope, core permeability, wave period, storm duration, wave grouping, etc.

This makes clear why during many years authors proposed di�erent formulae to estimate

damage on the armour layer due to wave attack. An overview of the most important formulae

can be found in table 2.1.

Until 1933 there didn't exist any method to calculate mound breakwaters. They were con-

structed based on experiences giving us qualitative criteria about the in�uence of the wave-

height, the angle of the slope, the weight of the armour elements, etc. Castro (1933) [1]

published the �rst formula to calculate the weight of rock materials of a mound breakwater.

In 1938, Iribarren [2] developed a theoretical model for the stability of armour units on a

slope under wave attack. Since his work, many studies about mound breakwater stability

were developed, showing di�erent formulae to predict damage in the armour layer due to wave

attack. The majority of those formulae assume a constant incident wave and initial damage

zero. The reality, however, shows that wave conditions are not stationary. That's why new

methods should be developed applying to no stationary processes. Many formulae, similar

to the formula of Iribarren, were developed (F.C. Tyrrel (1949), Mathews (1951) and Rodolf

(1951)) and in 1950 Iribarren and Nogales [3] generalized the formula by introducing the e�ect

of the depth and the period, using a modi�cation in the wave-height. Two years later Larras

(1952) [4] presented another formula taking into account the depth and the length of the wave.


Hedar (1953) marks up that it's necessary to consider two possible states to lose stability:

when the wave climbs on the slope before breaking and when the broken wave descends from

the mound breakwater.

The most frequently cited armour stability formula was published by Hudson (1959) [5] based

on the pioneering work of Iribarren. Hudson's formula was originally proposed for regular

waves, yet SPM (1973) and SPM (1984) [6] popularized the formula as well for irregular

waves using the equivalences H1/3 and H1/10 respectively as representative of the wave height

of irregular waves. Core permeability, wave period, storm duration, random waves, wave

grouping were not considered. Iribarren (1965) presented in the Navigation Conference the

relation of the friction coe�cient with the number of elements on the slope. He also limited

in this year the use of his formula by introducing, in an indirect way, the e�ect of the period

in the stability.

Carstens et al.(1966) [7] present the �rst results of tests on rock mound breakwaters with

irregular waves. Font (1968) veri�es empirically the in�uence of the storm duration on the

stability of mound breakwaters.

Battjes (1974) [8] introduces for the �rst time the parameter of Iribarren in the study of

characteristics of the �ow on smooth and impermeable slopes. Other experimental works in

the same line were done by Ahrens and McCartney (1975), Bruun and Johannesson (1976),

Bruun and Bünbak (1976).

An extensive investigation was performed by Thompson and Shuttler (1975) on the stability

of rubble mound revetments under random waves. One of their main conclusions was that,

within the scatter of the results, the erosion damage showed a clear dependence on the wave

period. The work of Thompson and Shuttler has therefore been used, as a starting point for an

extensive model research program. Analysis of the results from all of these tests has resulted

in two practical design formulae that describe the in�uence of wave period, storm duration,

armor grading, spectrum shape, grouping of waves, and the permeability of the core.

In 1976, PIANC [9], presented the most important used formulae and calculations of break-

waters until this time, showing the big di�erence in results between the di�erent methods.


The occured damages in the breakwaters in Bilbao (1976), Sines (1978) and San Siprian

(1979) showed the importance of the calculation of a mound breakwater and of the methods

to calculate the incident waves.

Whillock and Price (1976) [10] showed by interlocking elements, that the security margin be-

tween initiation of damage and destruction of the armour layer is very low, introducing for

the �rst time the concept "fragility" of the slope. Magoon and Baird (1977) [11] accentuated

the importance of the movements of the armour elements due to wave attack when the ar-

mour elements break, especially by the most slender elements with the highest interlocking

development.

Losada and Giménez-Curto (1979,a) [12] use the concept of interacting curves to analyze

the stability using the wave-height and the period and recognize the intrinsic arbitrariness of

the response of rock mound breakwaters. Losada and Giménez-Curto (1981) [13] use for the

�rst time the hypothesis of equivalence in the study of probability of failure and analyse the

in�uence of the duration in the probability of failure. In 1982 Losada and Giménez-Curto

[14] present a hypothesis to calculate the stability of quarrystone mound breakwaters with

non-perpendicular incident wave.

Lorenzo and Losada (1984) show, using results of �eld tests, laboratory tests and numerical

modelling, the fragility of the slopes with dolosse with big size, because of their structural

weakness. Those results can be generalized for slender elements showing interlocking.

Desiré (1985) [15] and Desiré and Losada (1985) study the stability of mound breakwaters with

paralelipepidic armour elements by doing many experiments with regular waves, observing a

big deviation in the results. They concluded that the results of the tests should be seen like

a statistic problem caused by the random nature of the variables (characteristics of the �ow,

resistance of the elements).

Van der Meer (1988) [16] proposed formulae including wave period, permeability and storm

duration. The cumulative e�ects of previous storms however were not included. Vidal et al.

(1995) [17] introduced a new wave height parameter Hn (The average of the n highest waves


in a sea state), to characterize breakwater stability under irregular waves and Jensen et al.

(1996) indicated that H250 is a suitable wave height parameter for irregular waves.

Medina (1996) [18] developed an exponential model applicable to individual waves of the storm,

including the non-stationary conditions of waves. Melby and Kobayashi (1998) [19] charac-

terized relationships for predicting temporal variations of mean damage with wave height and

period varying with time for breaking wave conditions.

Vandenbosch et al. (2002) [20] analyzed the in�uence of placement density on the stability of

a mound breakwater with two layers of concrete cube armour units. He showed that increase

of placement density not always means an increase of stability. An armour layer with a high

density can cause other failure modes, as there are displacement of the armour layer or the

lifting up of elements because of suppression.

Medina et al. designed in 2003 a Neural Network model applicable to non-stationary condi-

tions. Accordingly, new methods to be applied in non-stationary conditions are required to

avoid simplifying the concept of 'design sea state', which implies stationary conditions. Also

the project CLASH (2002-2004) was focussed in obtaining a neural network model to predict

overtopping on coastal structures (De Rouck et al.) [21].

Vidal et al. (2004) [22], showed that the H50 parameter, de�ned as the average of the 50

highest waves in the structures lifetime, can be used to describe the evolution of damage in

rubble mound breakwaters attacked by sea states of any duration and wave height distribution.

Gómez-Martín and Medina (2004-2006) [23] adjusted the wave-to-wave exponential model to

estimate the n50% parameter for rubble mound breakwaters, in case of rock slopes or slopes

with cubes. The model is also applicable in non-stationary conditions. In 2005 Gómez-Martín

and Medina [24] de�ned a new failure mode of mound breakwaters, named 'Heterogeneous

Packing', the most important failure mode in case of armour layers formed by cubes or concrete

elements. It is characterized by a decrease of porosity of the armour layer on some places and

increase on others, without extracting armour units. They also described a new methodology

'Virtual Net Method' to provide damage measurement, considering the di�erence in porosity

compared to the initial porosity of each of the zones of the armour layer.


Castro 1933 W = 0,704

(cotθ+1)2√cotθ−2/γr

· H3γr(γr/γw−1)3

Iribarren 1938 W = K(cosθ−sinθ)3 ·

H3γr(γr/γw−1)3

Tyrrel 1949 W = K(µ−tanθ)3 ·

H2Tγr(γr/γw−1)3

Matthews 1951 W = 0,0149

(µcotθ−0,75sinθ)2H3γr

(γr/γw−1)3

Rodolf 1951 W = 0,0162tan3(45−θ/2)

H2Tγr(γr/γw−1)3

Larras 1952 W =K·

(2πHL

sinh 4πzL

)3

(cotθ−sinθ)3γrH3

(γr/γw−1)3

Hedar: climbing waves 1953 W = K0

(µcosθ+sinθ)3H3γr

(γr/γw−1)3

Hedar: descending waves 1953 W = K(µcosθ−sinθ)3

H3γr(γr/γw−1)3

Hudson 1959 W = 1KDcotθ

H3γr(γr/γw−1)3

Table 2.1: Hydraulic stability criteria for the armour layer of a mound breakwater as cited in[1]

2.3 Analysis of the stability of a mound breakwater

2.3.1 General stability of a mound breakwater

To understand the structural stability of mound breakwaters, in the �rst place, the di�erent

reasons for loss of stability should be understood, and thus the di�erent failure modes have

to be de�ned.

Bruun (1979) [25] speci�ed eleven di�erent principal failure modes demonstrated in �gure 2.1.

1. Loss of armour units (increasing porosity).

2. Rocking of the armour units; breaking is due to fatigue.

3. Damage of the inner slope by wave overtopping.

4. Sliding of the armour layer due to a lack of friction with the layers below.

5. Lack of compactness in the underlying layers, causing excessive transmission of energy

to the interior of the breakwater; this might lift the breakwater cap and the interior

layers.


Figure 2.1: Mound Breakwater failure modes de�ned by Bruun

6. Undermining of the crone wall.

7. Breaking of the armour units caused by impact, simply by exceeding its structural

resistance or by slamming into other units.

8. Settlement or collapsing of the subsoil.

9. Erosion of the breakwater toe or the breakwater interior.

10. Loss of the mechanical characteristics of the materials.

11. Construction errors.

Those failure modes can be rearranged into �ve families of failure (Gómez-Martín, 2002) [26]:

� I Unit stability: the capacity of each piece to resist the movement caused by wave

action (1, 2, 3).

� II Global stability: the stability of the entire breakwater, or more speci�c, of the

entire armour layer, acting as one piece. It includes the movement of the armour layer

or the movement of big parts (4, 5, 6).

� III Structural stability: resistance of the elements or their material. This includes

the ability of the elements of resisting the tensions caused by transport, construction,

wave action, the used granular and the movements caused by currents (7, 2).


� IV Geotechnical stability: the resistance of the underground or the sensitivity to

erosion of the breakwater toe (8, 9).

� V Errors in the construction (10, 11).

The relative importance of every failure mechanism depends on di�erent factors, as there

are: intensity of the waves, depth of the mound breakwater, type of the ground, type of

construction materials, etc.

Loss of stability of the armour layer, being extraction of armour units out of the armour

layer or breaking of individual armour units by exceeding their structural strength and crest

overtopping of the breakwater are considered to be the most important failure modes of a

mound breakwater. Those failure modes have been intensively studied and play a dominant

roll in the design of a breakwater.

In this report, only the hydraulic stability of the armour units will be studied, more speci�cally

the loss of armour elements in certain zones of the breakwater slope, which is usually considered

as the main mode of failure and is classi�ed into the failure family of 'Unit Stability' in the

classi�cation of Gómez-Martín. This failure mode can be caused by two di�erent reasons:

the simple extraction of the armour units under wave attack, or their excessive settlement,

causing a heterogeneous packing. This last failure mode is proposed by Gómez-Martín and

Medina [24] and will be commented later in this chapter.

Once de�ned the di�erent types of damage, there's a need to specify the moment when a mound

breakwater is considered as damaged. Therefore, four damage levels will be distinguished,

de�ned by Losada et al. in 1986 [27], and completed by Vidal et al in 1991 [28] with the level

of Initiation of destruction (this is commented later in this Masterthesis in 6.4.2.2):

� Initiation of Damage (IDa)

� Initiation of Iribarren Damage (IIDa)

� Initiation of Destruction (IDe)

� Destruction (De)


2.3.2 Heterogeneous packing

2.3.2.1 Introduction

This project works with armour layers consisting of cubes or Cubipod elements. Those are

robust armour elements which means that in the �rst place the hydraulic stability, the capacity

of the elements to resist against movement due to wave attack supposing that they don't break,

will be studied. Their structural stability, however, may not be forgotten. The monolithic and

robust elements probably won't reach such a tensional situation able to break them, but the

elements can break partially, due to slamming between each other, decreasing their weight,

and thus decreasing their structural stability. An element in the armour layer can move in

three di�erent ways:

I: Pitching in their position in the armour layer. This is important when the structural

stability can be the origin of additional tensions on the elements.

II: Displacement by extraction out of the armour layer. The extraction of elements

out of their original position was during many years considered as the principal indicator of

the stability of an armour layer under wave attack and the stability calculations were based

on this failure mode (Fig. 2.2).

III: Packing of the elements as a result of small unit movements and frequent face-to-face

arrangements. This new failure mode is de�ned by Gómez-Martín and Medina [24] and is

called 'Heterogeneous Packing' also shown in �gure 2.2.

2.3.2.2 Heterogeneous packing

Heterogeneous packing is the most important failure mode in case of armour layers formed by

cubes or concrete elements and is characterized by a decrease of porosity of the armour layer

on some places and increase on others, without extracting armour units, but only by moving

them within the armour layer.

In tests, they observed that this failure mode tends to increase the packing density below the

still water level, which is balanced by a corresponding reduction in packing density above and


near the still water level. Heterogeneous Packing occurs always, but the intensity and the

relative importance of this failure mode depends on four main factors:

� Type of armour unit

� Di�erence between the initial porosity and minimum porosity

� Slope of the armour layer

� Friction coe�cient between the armour layer and the �lter layer

The Heterogeneous Packing has an e�ect similar to the erosion caused by extracting armour

units, because the reduction of the packing density near the mean water level can facilitate

the extraction of units from the inner layers. Thus, the armour layer is damaged by two

di�erent failure mechanisms: armour unit extraction and Heterogeneous Packing. In both

cases, the result is similar: a decrease in the number of armour units near the mean water

level. Studying the stability of the armour layer by wave attack, it's very important to take

this failure mode into account together with the extraction of elements.

To have extraction of an armour element out of the armour layer, the wave has to overcome

the friction and the interlocking between the elements in the armour layer and their own

weight. Friction is a microscopic type of resistance between di�erent elements; interlocking

refers to a macroscopic type of resistance, formed by the contact between the protuberances

of the elements.

If the height of the wave exceeds a critical point, extraction of elements or heterogeneous

packing of armour elements starts, and only their own weight o�er resistance to displacement.

Those extractions or Heterogeneous Packing stop when the wave decreases. The mound break-

water obtains a stable situation, called 'Partial Stability', which depends on the number of

displaced elements, the wave attack and his duration.

The moved elements are in an unfavourable situation. Their probability to displacement is

high. When the wave exceeds a certain value, the armour layer won't obtain a stable situation,

but develop until complete destruction occurs.

It's important to know that during this process, Heterogeneous Packing of the elements can


Figure 2.2: The two most important failure modes by mound breakwaters: extraction of armour

elements and heterogeneous packing. The classical view vs. the heterogeneous packing

view

increase the capacity of the armour layer in some places, but can also lead to important

disintegrations, causing damage.

2.3.3 Damage criteria

The classic de�nition declares damage of an armour layer as the percentage of displaced units

compared to the total number of units used to construct the slope. The classic failure criteria

are directly (extraction of armour units) or indirectly (changing in pro�le of the armour layer)

connected to lose or extract armour units due to wave attack as shown in the left side of

picture 2.2. This classic de�nition, however, doesn't allow generalizing the result, because

damage depends on the size of the armour layer.

A better de�nition was given by Van de Kreeke [29] and Oullet [30]. This de�nition consists

in comparing the displaced elements with the initial number of elements in a determined zone

of the breakwater slope near the mean water level.

Iribarren (1965) [31] proposed a clear damage de�nition for mound breakwaters. A mound

breakwater reaches his failure level when the �rst armour layer has been displaced in an area

su�ciently large to expose at least one armour unit of the layer below. If the breakwater

reaches this state, it is considered as seriously damaged, because wave action can damage the

second armour layer, and the underlayer will be in danger as well and total destruction of the

breakwater is impending.


In 1980 Paape and Ligteringen [32] mentioned that measuring the number or percentage of

blocks removed and displaced to the toe of the structure, is only valid for small damages

which is evenly distributed over the slope. With appreciable damage, it is important to

observe whether concentrations of block removal occur, which consequently a�ect the basic

idea of a two-layer armour cover and eventually even lead to exposure of the second layer

and core. Therefore, they proposed a damage classi�cation in function of the percentage of

displaced blocks and the e�ect of such removal on the armour layer. It is obvious that such a

classi�cation is subjective.

In general, two di�erent systems exist to quantify the damage:

� Quantitative criteria's: the number or percentage of displaced armour units is compared

to the initial ones.

� Qualitative criteria's: important changes in the morphology of the armour layer are

concerned.

A disadvantage of quantitative citeria's is that they don't give information about Hetero-

geneous Packing, which can be very important in situations with Cubipod elements in the

armour layer. The second method provides qualitative information about the damage level,

but has a principal disadvantage to be subjective. Concerning this facts, a new method for

damage estimation, taking into account the number of displaced elements and the changes

in porosity of the armour layer by Heterogeneous Packing, is necessary. Gómez-Martín and

Medina (2006) [24] present a new method for damage estimation: the Virtual Net Method.

An equivalent dimensionless damage measurement is used to take into account the di�erence

in porosity, in each zone of the armour layer, compared to their initial porosity. This method

is explained in 6.4.2.3. The method is complemented using qualitative criteria's considering

di�erent levels of damage: Initiation of damage, Initiation of Iribarren damage, Initiation of

destruccion and Destruccion. Those are explained further in 6.4.2.2.


2.4 Quantization of the stability

2.4.1 Formula to calculate the stability of a mound breakwater

As described in the short history, during the years, many formulae to calculate the stability

of a mound breakwater have been developed. The Shore Protection Manual (1984) [6], based

on the works of Hudson (1959) [5], proposes the next formulae to calculate the stability of a

mound breakwater:

W =1kD

H3

(Sr − 1)3γrcotα

(2.1)

Ns =Hs

∆Dn50= (KDcotα)1/3 ; ∆ = Sr − 1 and Dn50 = 3

√W

γr(2.2)

With:

W the weight of on individual element of the armour layer, in N

γr is the unit weight of the armour elements, in N/m3

H is the incident wave-height, in m

Sr is the speci�c gravity of the armour units, relative to the water at the structure

α is the angle of the structure slope, respective to the horizontal, in degrees

H is the design wave height at the structure, in meter

Ns the hydraulic stability coe�cient

KD is the hydraulic stability coe�cient, depending on many characteristics:

� Form of the element of the armour layer

� Number of layers of the armour layer

� Way of collocating the elements

� Roughness of the elements

� Interlocking between the elements

� Water depth near the structure (breaking or non-breaking)


� Part of the mound breakwater (head or body of the mound breakwater)

� Angle of the incident wave

� Porosity of the core

� Size of the core

� Width of the crest

� Other geometrical characteristics of the section

The values of KD need to be obtained experimentally, determining the wave-height that pro-

duces initiation of damage. The value KD takes into account many variables, where the most

important one is the used armour unit. Therefore, KD is an important characteristic for ev-

ery armour unit, as well to be able to use the Hudson design formula, as to provide a unit

characteristic that allows comparison with other units. SPM [6] resumed recommended KD

values in a table. They give the hydraulic stability factor in function of the type of the armour

unit, the number of armour layers, the way of collocation (uniform or random), the part of

the mound breakwater (head or body) and the water depth (breaking or non-breaking).

This method to obtain the KD values experimentally however, shows some shortcomings. KD

doesn't depend on the period, storm duration, wave grouping, etc. The prototype can be

di�erent from the real construction: the real construction method is not the same as in the

laboratory and the used materials can be very di�erent. Further, The wave-height for irregular

wave was not de�ned, SPM recomended H=H1/3 and later H=H1/10.

Chapter 3

Armour Units

3.1 Introduction

Originaly, harbours were built with wooden or stone constructions. The continuous increase

of the economy, however, meant the necessity of bigger harbours. Therefore, the harbours

were built more into sea, which led to an increase of the height of the attacking waves. The

design of the harbour evolved to constructions with a heavy rock outer layer. The continuous

increase of the attacking waves meant always a need for larger stones to guarantee the stability

of the construction. The size of natural stones has their limits, and design of arti�cial concrete

armour units was forced. The �rst elements were simple cubes, but soon, problems concerning

those elements were discovered. Nowadays, many di�erent breakwater armour units exist, each

with their own advantages and disadvantages.

The characteristics of the concrete armour elements have an important in�uence on the hy-

draulic stability of the mound breakwater. Further, the cost of the armour layer is an im-

portant part of the total cost of the breakwater. Those facts explain why improvement and

development of armour units is still an important subject of research.

In this chapter a historical overview of the development of the armour units for breakwaters

during the last 50 years is given. Further, di�erent ways to classify the existing elements are

discussed and lastly the new armour unit, the Cubipod, is introduced. The motivation and

concept of the design, with his advantages are explained.

18

Armour Units 19

Figure 3.1: Face to face �tting by cubes reducing the friction with the �lter layer

3.2 History: the armour units since the 50's

In the past 50 years a large variety of concrete breakwater armour units has been developed.

Today design engineers have the choice between many di�erent breakwater armour concepts.

However, in many cases standard type solutions are applied and possible alternative concepts

are not seriously considered. The most important and mentioned armour units in this part

are resumed in the table 3.2.

Until World War II breakwater armouring was typically either made of rock or of parallelepi-

pedic concrete units (cubes). The placement was either random or uniform. Breakwaters

were mostly designed with gentle slopes and relatively large armour units that were mainly

stabilised by their own weight. Those units have numerous advantages: a high structural

strength, cheap and easy to fabricate, store and put into place; furthermore the elements have

a low risk to progressive failure. But these units do have certain drawbacks that must be taken

into consideration. They have a low hydraulic stability (KD=6) and tend to settle to a regular

pattern. The layer becomes an almost solid layer which can lead to excess pore pressure and

lifting of the blocks. This also means an important loss of friction with the underlying layer

and can cause a sliding of the armour units. Another important disadvantage to mention is

the phenomenon of Heterogeneous Packing. This failure mode, without extraction of units,

tends to reduce the packing density of the armour layer near the still water level without

extracting armour units, but only by moving the units within the armour layer, caused by

unit movements and face-to-face �tting (Fig 3.1).

From the 50's the economical development and the increase of the dimensions of the tankers,

Armour Units 20

obliged us to realize depth mound breakwaters. Many laboratories in the world tried to develop

and patent new types of arti�cial breakwater armour units. The main objective was to design

elements with a high stability coe�cient to reduce the weight of the mantel elements and thus

the total cost of the structure.

In 1950 The Laboratoir Dauphinois d'Hydraulique in Grenoble introduced the Tetrapod, a

four-legged concrete structure and the �rst interlocking armour unit. The tetrapod is the �rst

of the "engineered" precast concrete armour units widely used all over the world produced by

many contractors and no longer protected by a patent. His main advantages are a slightly

improved interlocking compared to a cube element and a larger porosity of the armour layer,

which causes wave energy dissipation and reduces the wave run-up.

The tetrapod inspired similar concrete structures for use in breakwaters, including the modi�ed

Cube (US, 1959), the Stabit (U.K., 1961), the Akmon (Netherlands, 1962), the Dolos (South

Africa, 1963), the Seabee (Australia, 1978), the Accropode (France, 1981), the Hollow Cube

(Germany, 1991), the A-jack (U.S., 1998), and the Xbloc (Netherlands, 2001), among others.

A large variety of concrete armour units has been developed in the period 1950 - 1970. How-

ever, most of the blocks from those days have been applied only for a very limited number

of projects. These armour units are typically either randomly or uniform placed in double

layers. The governing stability factors are the units' own weight and their interlocking.

The Dolos was developed in the 60´s for rehabilitating the damaged breakwater at the Port

of East London in South Africa. Dolosse are armour units with a slender shape, a relatively

slender central section and long legs will face high stresses in the central part of the armour

block. These blocks have a high risk of breaking in the central part and broken armour units

have little residual stability and reinforcement should uneconomical.

The failure of the Sines breakwater (Portugal, 1978) who was constructed with dolosse in-

dicated that slender armour units, designed for maximum interlocking, provide insu�cient

structural stability and breakage of armour units may cause progressive failure. This event

set an end to the rapid development of elements with high stability coe�cient and reduced

weight.

Armour Units 21

More failures in the last two decades meant the end of the general con�dence and the optimism

in the classical techniques to design. The 80's meant a decade of big changes. The reasons of

failure were analysed and new methods of calculation and design were searched.

Single layer randomly placed armour units have been applied since 1980. The Accropode

(France, 1980) was the �rst block of this new generation of armour units and became the

leading armour unit worldwide for the next 20 years. The Accropode is a compact shape

and the basic concept of the unit was a balance between interlocking and structural stability.

The blocks are placed in a single layer on a prede�ned grid. The orientation of the block

has to vary; therefore Sogreah recommends various techniques for placement. However, sling

techniques and grid placing do not guarantee a perfect interlocking of the individual armour

units. Therefore relatively conservative KD values are recommended for design. Unfortunately,

Sogreah did not succeed to overcome these di�culties by developing a more reliable placement

procedure.

CoreLoc and A-Jack are further examples of this type of single layer randomly placed armour

units that have been developed subsequently. Hence, these blocks are more economical than

traditional double armour layers. The CoreLoc, developed by the US Army of Engineers in

1994, appeared to be more slender then the Accropode and to have a higher hydraulic stability.

After drop tests, it was found that the structural stability of the CoreLoc was signi�cantly

better than for dolos units because of his more compact central section. However he showed

with respect to structural stability, residual stability after breaking as well as ease of casting

and placement.

The A-Jack, introduced by Armortec (1997) consists of three long cement stakes joined at the

middle, forming six legs. It is a high interlocking armour unit that has been applied up to

know only for revetments and not for breakwater armouring. The elements are very slender

and the structural stability might be very critical if the blocks exceed a great size (1-2m3),

however the large KD value limits the block size and thus A-Jacks can be cost-e�cient for

temporary structures and moderate wave conditions.

The parallel development of a completely di�erent type of armour concept started in the late

60th. The armour layer consists of hollow blocks that are placed orderly in one layer. Each

Armour Units 22

block is tied to its position by the neighbouring blocks. Their hydraulic stability is not based

on weight or interlocking, but is extremely high as it is based on friction between the block

and the blocks around. The friction between uniformly placed blocks varies signi�cantly less

than interlocking between randomly placed blocks. Therefore a friction type armour layer is

more homogeneous than interlocking armour and very stable. The wave energy is dissipated

in the proper elements, in the internal voids of the blocks. These elements provide a �erce

reduction of the weight and a relatively high porosity of the armour layer, but on the other

hand some of the sections have to be reinforced due to their slenderness. As placement of

these elements is very di�cult under water, they are normally only applied in circumstances

where construction can be done above low water. Typical examples of these elements are Cob,

Shed and Seabee.

Another possible discussion concerning armour elements is reinforcement of slender units.

Treadwell and Wagoon (2006) [33] are of opinion that concrete armour units for coastal struc-

tures need reinforcement. Concrete armour units are believed to be one of the very few coastal

concrete structures that generally do not contain reinforcement. Concrete is a very strong ma-

terial in compression, but with very little strength in tension, especially during impact events.

The main bene�ts of reinforcement of concrete armour units are added strength during casting,

curing, moving, placing, and during all service loading conditions (including violent rocking

during severe storms) and avoidance of rapid failure, if indeed failure occurs at all. Given the

maintance problems and catastrophic failures that have been experienced by concrete armour

unit installations, it is clear that the added cost of reinforcement would be more than o�set

by reduced costs of maintance and repair and evaluations and the avoidance of the negative

economic impacts to revenue streams when coastal protection systems su�er severe damage.

Armour Units 23

Figure 3.2: A selection of the existing concrete armour units

Armour Units 24

3.3 Classi�cation of armour units

As there are over a hundred di�erent armour units, a manner to classify them is needed.

There are many criteria; armour units can be classi�ed according their shape, their placement

pattern, the risk of progressive failure, the number of layers, their structural strength and

the way they resist wave action. Each of those classi�cationsystems are described. All the

mentioned armour units can be seen in the table 3.2.

A �rst way to classifying armour units is by their shape as shown in table 3.1. This classi�cation

was made by Muttray, Reedijk, and Klabbers (2004) [34].

Shape Armour blocks

Cubical Cube, Antifer cube, Modi�ed cube, Grabbelar, Cob, Shed

Double anchor Dolos, Akmon, Toskane

Thetraeder Tetrapod, Tethrahedron, Tripod

Combined bars 2D: Accropod, Gassho, Core-Loc

3D: Hexapod, Hexaleg, A-Jack

L-shaped blocks Bipod

Slab type (various shapes) Tribar, Trilong, N-shaped block, Hollow square

Others Stabit, Seabee

Table 3.1: Classi�cation of breakwater armour units by shape [34]

The placement pattern of armour elements can be uniform or randomly. In case of robust

elements, random placement is suggested to guarantee the porosity of the armour layers and

to avoid the excess pore pressure inside the breakwater which may lift the blocks. If the

placement of the elements is random and there's no request concerning the orientation of the

individual elements to obtain a good disposition, the construction is much easier then in case

of uniform placement.

Concerning the risk of progressive failure, armour units can be classi�ed in slender blocks and

compact blocks.

In case of slender armour units, the stability is mainly due to interlocking and the average

Armour Units 25

hydraulic stability is large. However, the variation in hydraulic resistance is also relatively

large and the structural stability is low. Therefore slender blocks shall be considered as a series

system with a large risk of progressive failure, because if they break in parts, the hydraulic

stability sharply decreases causing simultaneous loss of weight and interlocking.

The stability of compact blocks is mainly due to the own weight. The structural stability is

high and the variation in hydraulic stability is relatively low. Thus, the armour layer can be

considered as a parallel system with a low risk of progressive failure.

The elemens can be placed in one or two layers. Single armour layer is more cost e�cient

due to the reduced number of armour blocks. It means saving concrete and lower costs for

fabrication and placement of blocks. Single layer placement also has technical advantages,

there is less rocking then in double armour layer and therefore a lower risk of impact loads

and breakage . Double armour layers do not provide additional safety against failure -except

for compact armour units with large structural stability and limited interlocking- because the

second layer tends to create breaking and is sensitive to rocking, thus the structural integrity of

the armour units is jeopardized. The placement in two layers on �at slopes is an uneconomical

solution.

Armour elements can resist wave action by their own weight, by interlocking or by friction.

In case of slender armour units, the stability is mainly due to interlocking and the average

hydraulic stability is large, however, the structural stability is low. The stability of compact

blocks is mainly due to the own weight. The average hydraulic stability is low. However, the

structural stability is high. Hollow elements will resist wave action mainly by friction.

A more general overview, combining di�erent classi�cation criteria, is proposed by Bakker et

al. (2003) [35] and is shown in table 3.2. He includes criteria for placement pattern (random or

uniform), number of layers (single or double layer), shape (simple and complex) and domimant

method of hydraulic stability (resisting wave action by own weight, interlocking or friction).

Armour Units 26

Placement Number Shape Stability factor

pattern of layers Own weight Interlocking Friction

double layer simple

Cube

Antifer cube

Modi�ed cube

complex Tetrapod, Akmon, Tribar, Tripod

Random Stabit, Dolos

single layer simple Cube

A-Jack

Accropode

Core-Loc

complex accropode

Uniform single layer simpleSeabee, Hollow

Cube, Diahitis

complex Cob, Shed

Table 3.2: Classi�cation of armour units by shape, placement and stability factor.

A common problem in the design of armour units is the need to choose between higher hy-

draulic stability and higher structural strength. Armour units can increase their hydraulic

stability by increasing their own weight, interlocking and higher friction with the inner layer.

Interlocking and a higher friction usually mean a signi�cant reduction in structural strength.

As a general rule, the stability coe�cient, KD increases from the massive to the slender cate-

gory; however this means a decrease of the structural strength.

A classi�cation by structural strength of the units is done by Mijlemans in 2006 [36]. Elements

can be subdivided in three groups: robust units that dispose of a very high structural strength,

fragile armour units with low structural resistance and an intermediate group that provides

a reasonably high structural stability. The classi�cation of Mijlemans (2006) is also based on

the placement method (number of layers and placement pattern) and creates in this way ten

families of arti�cial concrete armour emelents as shown in table 3.3.

The robust units have a massive form that provides a high structural strength. The large and

Armour Units 27

compact cross-sections cause small tensile stresses which decreases the risk of unit breaking.

They resist wave attack mainly by their own weight and the average hydraulic stability can

be considered rather low. Because of their high structural stability and their low variation in

hydraulic stability, they present a low risk of progressive failure.

Fragile units have a very low structural stability because of their limited cross-sectional areas.

The most important stability factor is interlocking which provides them with a high average

hydraulic stability. Their variation in hydraulic stability however is quite high and together

with the low structural stability, the risk of progressive failure is high. Fragile elements can

be subdivided into hollow units, where the interlocking is provided by their reciprocal friction,

and slender solid units where the slender members interlace with one another.

The intermediate group is originated to combine the high structural stability of robust ar-

mour units with the interlocking characteristics of the fragile elements. Their form provides

an amount of resistance by interlocking, but avoids also too slender cross-sectional areas to

maintain a high structural strength. They have a rather massive form, therefore their dom-

inant hydraulic stability factors are their own weight and interlocking. They provide a high

hydraulic stability and an intermediate structural resistance which decreases their risk of pro-

gressive failure in comparison with the fragile units above.

Structural resistance

Placement method Robust Intermediate Fragil

Random multiple layers group 1 group 2group 3

group 4

one layer group 5

Uniform multiple layers group 6 group 7 group 8

one layer group 9 group 10group 11

group 12

Table 3.3: Classi�cation of armour units by placement method and structural strength (Mijlemans,

2006)

Armour Units 28

3.4 A new armour unit: The Cubipod

3.4.1 Introduction

The Cubipod is a new armour unit for the protection of maritime structures invented by Josep

R. Medina and M. Esther Gómez-Martín, patented in 2005 by the Laboratory of Ports and

Coasts of the UPV (Patent number: P200501750) and licensed by SATO.

Figure 3.3: A new armour element: the Cubipod

3.4.2 Idea

Numerous armour units have shown high hydraulic stability such as Tetrapods, Dolos, Ac-

cropodes, Core-locs, X-blocks, etc. which permit a reduction in the concrete armour unit

weight, however they have a low structural strength. The collapse in Sines (Portugal) and the

severe damage in San Ciprián (Spain) showed us that the structural strength is an important

parameter in the choice of the armour element.

Randomly placed massive units with a simple shape like cubes or parallellepipedics are widely

used because of their numerous advantages: structurally robust, cheap and easy to fabricate,

manufacture, store and put into place; furthermore there is a low risk to progressive failure.

Nevertheless, these units do have certain drawbacks that must be taken into consideration.

Armour Units 29

They have a low hydraulic stability (KD=6 for cubes) and a high Heterogeneous Packing

failure mode.

3.4.3 Concept

The Cubipod is designed to form the protective layer of mound breakwaters, seawalls and piers

in order to protect coasts, hydraulic or maritime constructions or in general to resist wave

breaking. The aim of the new armour unit is to bene�t from the advantages of the traditional

cubic block, like the high structural strength and easy placement, but to correct the drawbacks

by preventing self packing and increasing the friction with the �lter layer. The new element

is a massive cubic element with equal protuberances on every side which have the form of

truncated pyramids with a square section. Preferably the size of the protuberances had to

be small in comparison with the cube or parallelepiped. Its principal function should be to

avoid settlement while the structural strength and hydraulic stability of a cube is maintained.

Therefore, the total volume of the protuberances should be an order of magnitude lower than

the volume of the basic element; e.g. not exceed 15% of the volume of the basic element

without protuberances. The �nal result is shown in �gure 3.3.

Robustness and high structural strength The design of the unit is based on the cube

in order to obtain his robustness. The cross-sectional areas are large and not slender, that's

why the Cubipod has a high individual structural strength. In order to assess the structural

strength of this new armor unit, overturning, free fall and extreme free fall tests have been

carried out. The Cubipod armour units were able to withstand higher drops than did the

conventional cubic blocks [37].

High friction with the �lter layer Cubic elements tend to place their sides parallel to

their underlying layer, which means a decrease of the friction between the armour layer and

the �lter layer. In case of Cubipods, the protuberances penetrate in the �lter layer and provide

an important increase of the friction with this layer.

Face-to-face �tting The protuberances avoid sliding of the armour elements. Due to this,

fact face-to-face �tting and the loss of elements above the still water level is reduced. This

Armour Units 30

Figure 3.4: Drop test results of Cubipods compared with cubes showing the lost weight

Figure 3.5: Penetration of the Cubipods in the armour layer

Armour Units 31

Figure 3.6: The separating e�ect of the protuberances avoiding the face-to-face arrangement

means that Cubipods reduce the Heterogeneous Packing failure mode of the armour layer

compared with the former used cube elements. The separating e�ect of the protuberances

avoiding this face-to-face arrangement is showed is �gure 3.6.

Hydraulic stability The hydraulic stability of Cubipods is higher than of cube elements

thanks to higher friction with the �lter layer and reduce of the Heterogeneous Packing as

explained above. This is proved in earlier tests in deepwater conditions [38]. This means a

reduction of the loss of elements above the upper parts and a lower run-up and overtopping.

Armour Units 32

Figure 3.7: Example of placement in a depository of Cubipods

Figure 3.8: The casting system designed by SATO and the tongs for movement and manufacture

Easy casting, e�cient storage and handling The Spanish construction company SATO

has designed a casting system and specially adapted tongs for the e�cient movement and

manufacture of Cubipods (Fig 3.8). Thanks to this system the fabrication can be done easy

and fast [?]. Thanks to their form, the storage can be done e�ciently, using little space (Fig

3.7). As the placement of the Cubipods is random and there's no request concerning the

orientation of the individual elements to obtain a good random disposition, the placement of

the elements is much easier then in case of uniform placement.

Chapter 4

Wave height in breaking conditions

4.1 Introduction

As the majority of mound breakwaters are built in shallow waters, a study of the behaviour

of waves in breaking conditions may be important knowing that those di�er a lot from the

conditions in deepwater. The height of waves is an important factor in�uencing the design of

coastal constructions. An overly conservative estimation can greatly increase costs and make

projects uneconomical, whereas underestimation could result in structural failure or signi�cant

maintenance costs.

In this chapter, �rst, general information will be given about breaking waves: the di�erent

types are shortly discussed. Some existing theories are presented to estimate the wave height

distribution in shallow waters followed by formulae to calculate the maximum wave height in

breaking conditions. In the next chapter, showing the results, a short comparison between the

obtained maximum wave height in the executed experiments and the existing theories is done.

The goal of this chapter is not to propose new formulae to calculate breaking characteristics,

but to give an overview of existing models and to compare di�erent theories with the measured

results in the laboratory experiments.

33

Wave height in breaking conditions 34

4.2 The surf zone

As waves enter shallow water, they slow down, grow taller and change shape. At a depth of

half its wave length, the rounded waves start to rise and their crests become shorter while

their troughs lengthen. Although their period stays the same, their overall wave length short-

ens. The 'bumps' gradually steepen and �nally break in the surf. There is a distinct di�erence

between the oscillatory wave motion before breaking and the turbulent waves with air entrain-

ment after breaking. In case of actual sea waves, some waves break far from the shore, some

at an intermediate distance and others approach quite near the shoreline before breaking. In

coastal waters therefore, wave breaking takes place in a relatively wide zone of variable water

depth, which is called the wave breaking zone or the surf zone.

4.3 Types of breaking waves

There are four types of breakers in the surf zone (Fig 4.1); spilling, plunging, collapsing and

surging. The slope of the beach and the types of waves approaching the surf zone determine

which type of breaker is going to be predominant.

Spilling In this type of wave, the crest undergoes deformation and destabilizes, resulting in

it spilling over the front of the wave. Only the top portion of the wave curls over. Light foam

tends to appear up the shore. It occurs most often on gentle beaches and is usually the most

observed type of wave.

In a spilling breaker, the energy which the wave has transported over many miles of sea is

released gradually over a considerable distance. The wave peaks up until it is very steep but

not vertical. Only the topmost portion of the wave curls over and descends on the forward

slope of the wave, where it then slides down into the trough. This explains why these waves

may look like an advancing line of foam.

Plunging The wave peaks up until it is an advancing vertical wall of water. The crest of

the wave advances faster than the base of the breaker, curls over and crashes into the base of

the wave, creating a sizable splash. It tends to happen most often when the gradient of the


sea �oor is medium to steep or from a sudden change in depth (a rock ledge or reef). It is also

a feature of breaking waves in o�shore conditions. These type of waves arise when the steep

gradient of the sea �oor or ledge is angular to the approaching swell direction.

In a plunging breaker, the energy is released suddenly into a downwardly directed mass of

water. A considerable amount of air is trapped when this happens and this air escapes

explosively behind the wave, throwing water high above the surface. The plunging breaker is

characterized by a loud explosive sound.

Collapsing Collapsing waves are a cross between plunging and surging, in which the crest

never fully breaks, yet the bottom face of the wave gets steeper and collapses, resulting in

foam.

Surging On steeper beaches, a wave might advance up without breaking at all. It deforms

and �attens from the bottom. The front of the wave advances up towards the crest, creating

re�ection.

Iribarren's number The deepwater Iribarren number (Iribarren and Nogales, 1949) Ir =

tan(α)/√H/L0, also called the breaker parameter describes a certain type of wave breaking

and contains a combination of structure slope and wave steepness: s0 = H/L0 (table 4.1).

For the executed tests we �nd numbers of Iribarren with values between 2 and 5. This is

because the slope is the mound breakwater is rather high (compared to the slope of a beach).

Breaking due to the mound breakwater will happen by collapsing or surging. As we are in

shallow waters with a horizontal bottom, the wave breaking taking place before the breakwater

will happen as spilling or plunging.

Breaking type spilling plunging collapsing surging

Ir Ir < 0, 5 0, 5 < Ir < 2, 5 2, 5 < Ir < 3 Ir > 3

Table 4.1: Type of breaking in function of the number of Iribarren


Figure 4.1: Types of breaking waves

4.4 Models to estimate the wave height distribution

In deep water, the approximately linear behaviour of the waves allows for a theoretically sound

statistical description of the wave characteristics, based on a Gaussian distribution of instan-

taneous values of surface evaluation, resulting in a Rayleigh distribution of wave heights. In

shallow water, the wave behaviour is more complicated and the knowledge of the statistical

description of wave �eld characteristics is more limited. The distribution before wave break-

ing can be approximated as being Rayleighan, which means that a group of random waves

entering the surf zone is assumed to have a Rayleigh distribution. Among the waves obeying

that distribution, those with height exceeding the breaking limit will break and cannot occupy

their original position in the wave height distribution. Breaking causes a truncation of the

waveheight distribution.

Several authors have developed wave height distributions that modify the Rayleigh distri-

bution of deepwater waves to take into account wave shoaling and breaking. Two di�erent

kind of models can be distinguished to account for the portion of energy retained by the broken

waves:

� The �rst type supposes that the energy from the broken waves is concentrated in the

breaking wave height. All the broken waves will have the breaking wave height in the

sur�ng zone (Fig ??).


Figure 4.2: Distribution of the wave heights by breaking, concerning that all the broken wave heights

will have the breaking wave height in the sur�ng zone

� The second type presents truncated wave height distributions that distribute the energy

from the broken waves back over the smaller wave heights in the distribution.

Collins (1970), Mase and Iwagaki (1982) and Dally and Dean (1986) presented a method to

calculate the distribution of the heights of breaking waves in shallow water. Given a sequence

of wave heights and periods and direction at some o�shore location, or a joint probability

distribution of those variables, they apply a monochromatic wave model for shoaling and

breaking to calculate the onshore transformation of that monochromatic wave class. These

methods, however, are algorithmic and do not result in explicit expressions for further analyses

or extrapolation to low probabilities of exceedance.

Another approach consists of making empirical adaptations to the Rayleigh distribution of the

wave heights to allow for the e�ects of shallow water and breaking, resulting in explicit ana-

lytical expressions. Glukhovskiy (1966) proposed a distribution for shallow waters by maken

the exponent an increasing function of the wave-height-to-depth ratio. For su�ciently low

wave height-to-water depth ratio, the distribution becomes a Rayleigh distribution.

Tayfun (1981) presented a theoretical model for the distribution of wave heights, including the

e�ect of wave breaking, based on a narrow-banded random phase model with a �nite number

of spectral components.

The distributions given by Glukhovskiy an Tayfun are both point models, yielding a local wave

height distribution for given local depth and wave parameters (lowest two spectral moments).

The Rayleigh distribution gives a poor description of the measured wave height distribution.

It underestimates the lower wave heights and overestimates the higher ones. The Glukho-


viskiy distribution yields a better approximation, however, in general, this distribution still

overestimates the extreme wave heights and underestimates the lower wave heights on shallow

foreshores.

Battjes and Groenendijk (2000) [39] proposed a composite Weibull wave height distribution

to give a better description of the measured wave height distributions in shallow waters. The

wave height distributions on shallow foreshores show a transition between a linear trend for

lower heights and a downward relation for the higher waves. This abrupt transition does not

lend itself to a distribution with one single expression and one shape parameter. Therefore

a combination of two Weibull-distributions was assumed, each having a di�erent exponent,

matched at the transition height Htr. The model predicts the local wave height distribution

in shallow foreshores for a given local water depth, bottom slope and total wave energy with

signi�cantly accuracy than existing models.

4.5 Maximum wave height in breaking conditions

As the wave height is one of the most important factors in�uencing the design of a mound

breakwater, over the years, many equations have been proposed to express the breaker height/breaker

depth ratio as a function of other variables. Those models however, do not employ all the

variables a�ecting the breaker height and depth, with the result that they apply only to limi-

ted conditions. Here, some models are explained, mentioning that this list is not complete at

all as there exist many formulae to calculate breaking characteristics.

Keulegan and Patterson (1940) [40] noted that the Hb/db ratio is related to wave breaking

which they considered to take place at values between 0,71 and 0,78. This gives us a simple

formula to calculate the breaking height, because it does not take into account the bottom

slope α, neither the wave period T.

Collins (1970) [41] was among the �rst to consider the e�ect of the bottom slope on wave

breaking, but did not take other variables into account. His equation which yields a ratio of

0,72 over a horizontal bed, increases to 1,21 for a 5O slope.


Hb

db= 0, 72 + 5, 6tanα (4.1)

Weggel (1972) [42] published one of the most useful equations. He considered the e�ect of the

sea �oor slope α in addition to the gravity constant g and wave period T. We can see however,

that the function becomes independent of the period T if the sea bottom is horizontal (E2=0).

His equation is valid for tanα ≤ 1.

Hb

db= E1 −

E2Hb

gTw2 (4.2)

E1 =1, 56

1 + e−19,5tanα

E2 =43, 75

1 + e−19tanα

Komar and Gaughan (1973) [43] derived a semi-empirical relationship from linear wave theory,

where the subscript 0 denotes deepwater conditions (Fig 6.3). This equation takes into account

the wave period T, using the formula of Airy for L0, but does not take the bottom slope into

account, neither the water depth in shallow water.

Hb

H0= 0, 56

(H0

L0

)−1/5

(4.3)

Sakai and Battjes (1980) [44] plotted a curve of the wave breaking limit as function of Hb/H0

against H0/L0 (Fig 6.3). They also only take into account the wave period T, but do not

take into account the bottom slope neither the water depth in shallow water. This curve is

described by the following equations:

Hb = H0

[0, 3839

(H0

L0

)−0,3118]

whenH0

L0< 0, 0208

Hb = H0

[0, 6683

(H0

L0

)−0,1686]

when 0, 0208 ≤ H0

L0< 0, 1 (4.4)

Hb = H0 when 0, 1 ≤ H0

L0


Komar (1998) proposed two seperated equations for Hb and db, where S is the sea �oor

gradient.

Hb = 0, 39g0,2(TH0

2)0,4

(4.5a)

db = Hb

1, 2

SHbL0

0,5

0,27 (4.5b)

Experimental work (Shore Protection Manual, 1984 [6]; Demirbilek and Vincent, 2002) for

waves breaking over di�erent bottom slopes with wave periods between 0s - 6s resulted in a

formula showing the dependance of the water depth and bottom slope:

Hb = db(−0, 0036α2 + 0, 0843α+ 0, 835

)(4.6)

Le Roux (2006) [45] presents approximations providing a very simple method to estimate wave

parameters and using the wave period as fundamental parameter because it is assumed to be

constant in all water depths. The expressions apply to smooth bottom pro�les without ridge

and runnel systems and assuming an absence of marine currents. As a wave begins to shoal

under these conditions, its height decreases initially and then increases shortly before breaking

whereas the wavelength decreases up to breaking. The wave height Hw in any water depth

changes in accordance with the deepwater wave height H0, wavelength L0 and water depth d:

Hw = H0

[A exp

(H0

L0B

)](4.7)

where

A = 0.5878(d

L0

)−0,18

whend

L0≤ 0, 0844 (4.8)

A = 0.9672(d

L0

)2

− 0.5013(d

L0

)+ 0, 9521 when 0, 0844 ≤ d

L0≤ 06 (4.9)

A = 1 whend

L0> 06 (4.10)

B = 0, 0042d

L0

−2,3211

(4.11)


By replacing Hb with Hw and db with d in equation 4.6 and using speci�c of H0 and L0,

changing the waterdepths simultaneously in equations 4.7 and 4.6 until the breaker height Hw

coincides, the breaker height and depth for both developing and Airy waves over any bottom

slope can be calculated.

Examining Hb for di�erent wave periods shows that:

Hb =Lb16

=gTw

2

48π(4.12)

Among Goda [46], however, the breaking limit for random sea waves should be allowed a range

of variation because even a regular wave train exhibits some �uctuation in breaker height and

a train of random sea waves would show a greater �uctuation owing the variation of individual

wave periods and other characteristics. Therefore wave breaking is assumed to take place in

the range of relative wave height from x2 to x1 with a probability of occurrence which varies

linearly between the two boundaries. With this assumption, the portion of waves which is

removed from the original distribution due to the process of breaking is represented by the

zone of slashed lines shown in �gure 4.3 The heights of individual random waves after breaking

are assumed to be distributed in the range of nondimensional wave heights between 0 and x1

with a probability proportional to the distribution of unbroken waves.


Figure 4.3: Distribution of the breaking wave heights over the distribution of the unbroken waves

(Goda [46])

Chapter 5

Experimental setup

5.1 Introduction

In this chapter, the experimental setup of the hydraulic model tests will be discussed. First

of all, the test equipment will be presented, including the wave �ume, the system used to

generate the waves, the di�erent measurement sensors and the data processing system. Next

the calibration of the wave generator and the experimental design of the models will be set out,

starting with the theoretical characteristics of the model. As the theoretical values are not

the real values for the model, the practical design values of the model will presented, together

with the construction method and the position of the wave gauges. This experimental design

is concluded with the realized experiments, the characteristics of the experiments and the

methodology used for the tests. To end the chapter, the method used to analyse the data is

set out.

5.2 The Test Equipment

The experiments are performed in het Laboratory of Port and Coastal Engineering to inves-

tigate the hydraulic stability of Cubipods in breaking conditions. This laboratory disposes of

a 2D wind and wave �ume with sensors gauging the position to control the exact parameters

of the experiments.

43

Experimental setup 44

Figure 5.1: Longitudinal section of the 2D wave-�ume

5.2.1 2D Wave Flume

The 2D wave �ume has a square cross-section of 1.2m x 1.2m and is 30 m long. In the centre

of the wave �ume, the bottom shows a gentle upward slope (4%; tanα = 1/25) over 6,15m,

hence the water depth near the model is 25 cm less than the water depth near the wavemaker.

On the raised �oor the model is put. A detailed plot of the total test setup within the wave

�ume is shown in Appendix B.

The slope and the foreshore are intended to stabilize the return �ow during the tests and if

not present, the translational movements of the water volumes would result in an elevation

of the water level on one side of the canal. This slope and platform assure the recirculation

of the water in the �ume. Another important advantage from the upward slope of the canal

�oor is that it permits the wave generation to occur at a higher water depth than the water

depth near the model, and thus attack the model with higher waves, without the limitation

of wave breaking at the wavemaker that occurs in �umes with a uniform �oor.

The water depth used for the experiments is between 55 cm and 65 cm near the wave generator

and between 30 cm and 40 cm near the model. The model is placed at a distance of . . .m

from the wave generator slab (measured at the toe of the breakwater) and is built on a scale

of 1/50.

5.2.2 Wave Generation System

On one of the ends of the �ume, a wave generating system is constructed. It consists of a

metal slab that moves horizontally by aid of a electronic piston. This movement is transmitted


on the water.

The piston is attached to the upper part of the paddle which means that a strong momentum is

introduced in the vertical slab when moving the water mass. However, a rigid steel frame forces

the paddle to move equally in a horizontal way on bronze rolls sliding on steel rail tracks. The

hydraulic compressor provides oil under pressure to a piston that moves the metal slab which

transmits its movements on the water. The movement of the piston is controlled by a valve,

which is guided by a position gauge communicating with the central electronic-informatics

system and transmitting the necessary corrections to obtain the correct movement.

Hydraulic model testing of wave impact on structures is often hampered by wave re�ection

from the test structure, here a mound breakwater. The wavegenerator has a theoretical

movement to generate a certain wave. As the re�ected waves return to the wavemaker, they are

usually re-re�ected, which results in an uncontrollable, most undesirable nonlinear distortion

of the desired waves impinging on the test structure, because the wavegenerator keeps having

the same movement.

Therefore, the wave generator is provided with an Active Wave Absorption Control System

(AWACS). AWACS is a digital control system, which enables wavemakers to generate the

desired waves and, at the same time, absorb spurious re�ected waves. The system provides

superior wave generation accuracy in hydraulic �umes. The used system in the laboratory is

DHI AWACS2, from Denmark.

The principle of the AWACS is to measure the surface elevation (waves) by two installed

wave gauges integrated in the paddle front. The measured waves are the superposition of

the desired waves and the re�ected waves returning to the wavemaker. The measured waves

are compared with the speci�ed, desired waves. By use of the digital recursive �lter of the

AWACS the re�ected waves are identi�ed and absorbed by the wavemaker. Hereby, spurious

re-re�ection from the wave paddle is eliminated.

Photos of the wave generation system are shown in �gure 5.2. The detailed working of the soft-

ware to manage the AWACS and to generate the waves in the �ume is explained in Appendix

C.


Figure 5.2: Wave generation system in the LPC wave �ume and setup of active wave absorption

system


5.2.3 Wave Measurement

The measuring system consists out of wave gauges, run-up sensors and a measurement system

for the erosion of the armour layer.

Wave Height The wave height is measured by wave gauges(Fig 5.3). They consist of two

vertical parallel conductors that work as a dielectric. The conductors dip into the water. The

current that �ows between the wires is proportional to the depth of immersion. The current

is noticed by an electronic circuit providing an output voltage. This output is proportional to

the instantaneous depth of immersion, the wave height in cm above the mean water level.

This type of gauges is very reliable in calibration and linear in the transformation of the data.

The output voltage can be calibrated in terms of the wave height by varying the depth of

immersion of the probe in still water by a measured amount and noting the change in output

signal.

The gauges have to be calibrated every day before starting the experiments, to intercept

the changes in water level in the �ume caused by leaks and the climatically changes being

change in temperature or humidity. These changes can a�ect on the working of the gauges

signi�cantly. To allow this calibration, the gauges are connected with the electronic equipment.

The measured data are sent to the computer which translates the signals in wave heights in

relation to the average water level. The sending of the data happens at a sampling frequency

of 20Hz.

Run-up A Step-Gauge Run-up System constructed by the University of Ghent is used to

measure the run-up (Fig 5.3). The electrodes of di�erent length are placed one behind the

other, in this way they follow the pro�le of the breakwater. The distance between the armour

units and the gauge can be set to less than 2mm, without touching the Cubipods. The working

of a step-gauge is very simple. Each electrode is connected to a circuit which detects if the

electrode is dry or wet. There are two analogue outputs: the �rst gives a voltage which

corresponds to the position of the highest electrode that still makes contact with the water,

the second gives a voltage that corresponds to the number of electrodes that are wet. The

measured results of the Steup-Gauge Run-up System are not used in this Masterthesis.


Figure 5.3: Wave gauges for wave measurement and Step-Gauge Run-up Measurement System (S-

GRMS) constructed by University of Ghent

Above this Step-gauge System, visual support is given by a person and a camera next to the

canal. Accomplishing every test, there's a person looking to perceive the run-up with help of

the measuring rod on the wall and there's a camera next to the canal �lming the right side of

the model through the glass wall.

Erosion of the armour layer Measuring of the erosion of the armour layer is done as

described in (Gómez-Martín and Medina) [24] and is based on the method of the virtual

mesh. After every test, pictures are made of the armour layer with a camera that is placed on

a standard over the wave �ume. Those pictures are used to measure the erosion of the armour

layer as explained in 5.4.4.4.

5.2.4 Energy dissipation system

On the other side of the canal there is an energy dissipation system. This system consists

of �ve groups of three grooved metal frameworks, and a plastic perforated plate. The metal

frameworks have three di�erent porosities: 70%, 50% and 30%, with the highest porosity

starting at the side where the wave approaches. A �rst group of three frameworks with 70%

porosity is followed by two groups with a porosity of 50%. The �rst of these two groups has

many and thin bars, the second has the same porosity but less bars, and thus the bars and

voids are wider. The fourth and �fth group have a porosity of 30% and again, the �rst is �ner


Figure 5.4: Wave energy dissipation system in the LPC wave �ume

than the secons one. The voids between the three frameworks of this group have been �lled

with quarrystone.

5.2.5 Data Processing

In the central computer situated in the o�ce area of the laboratory, the correct data is

inputted. This data is sent to the wave generator to generate the correct wave. Afterwards

the measured data by the wave gauges and the Step-Gauge Run-up System, are sent to the

same central computer to analyse these results. This is explained more in detail in Appendix

C.


5.3 Calibration of the wave �ume

Before starting the experiments on the breakwater model, it is important to know if the

wave generation in the laboratory is representative for those that really need to be generated.

If the required conditions are not represented accurately, this will a�ect the results of the

experiments. The factor that needs to be veri�ed to calibrate and control these conditions is

the wave generation. Calibration experiments in the wave �ume were carried out to examine

these e�ects before starting the actual model experiments. The energy absorption system

AWACS in the wavemaker guarantees a constant wave generation.

To control the operation of wavemaker, the theoretical dates (wave height and wave period)

of the lanced wave have to be compared with the measured wave height and wave period near

the wavemaker.

5.4 Experimental Design

5.4.1 Physical characteristics of the studied model

The used model is a mound breakwater with an inner slope of 4:3 and an outer slope of

3:2. Although no speci�c prototype breakwater is considered, reference is made to prototype

values. A basic scale factor of 1:50 is considered, which corresponds with real Cubipods of

16ton and standard Mediteranean dimensions. The mound breakwater consists of three parts.

The core of �ne gravel (type G2) forming the base of the mound breakwater, a �lter layer

(type G1) forming the underground for the main armour units and the armour layer existing

of the Cubipods (or cubes). The armour units reach until the toe of the structure.

The Cubipods are made of resin and have a density of 2,30t/m3, they weight 128g and have

a theoretic equivalent cube size of 3,82cm. The cubes, also made of resin, weight 147,2g each

and have a cube size of 4,00cm, slightly bigger than the size of the Cubipods. The calculation

of the theoretic equivalent cube size and theoretic volume using the known dimensions of the

Cubipods is shown in table 5.1. The theoretical characteristics of all the used materials are

shown in table 5.2. The proposed porosity of the armour layer is 41%.


cubes Cubipods

L cube [cm] 4 3,575

h pyramid trunc [cm] 0 0,894

V cube [cm3] 64 45,691

V pyramid trunc [cm3] 0 1,666

V total [cm3] 64 55,686

D50 [cm] 4 3,819

Table 5.1: Calculating the theoretic equivalent cube size and the theoretic volume of the Cubipods

Model of the cubes Model of the Cubipods

D50 [cm] density [t/m3] weight [g] D50 [cm] density [t/m3] weight [g]

Armour layer 4,00 2,3 147,2 3,82 2,30 128

Filter (G1) 1,80 2,70 16 1,80 2,70 16

Core (G2) 0,70 2,70 0,90 0,70 2,70 0,90

Table 5.2: Theoretic characteristics of the used materials

The considered water depths vary between 30cm and 42cm near the model. The crest is

supposed to be high enough so that overtopping is not considered. Only tests in breaking

wave conditions were carried out: the breakwater is assumed to be in shallow water.

Five di�erent models, each with the same core- and �lterconstruction, will be considered (Fig

5.5 and Fig 5.6):

� double layer of Cubipods: C2

� single layer of Cubipods: C1

� single layer of cubes covered by a single layer of Cubipods: CB

� double layer of Cubipods with toe berm: C2B

� single layer of Cubipods with toe berm: C1B


Figure 5.5: Cross section of the studied models: 2 layers of Cubipods (C2), 1 layer of Cubipods (C1),

1 layer of cubes covered by one layer of Cubipods (CB)


Figure 5.6: Cross section of the studied models: 2 layers of Cubipods with toe berm (C2B), 1 layer

of Cubipods with toe berm (C1B)


First the tests C2 will be considered. Afterwards, the second layer is removed and the �rst

layer of C2 will be used to execute the experiments C1. To realize the tests CB, in the

beginning only the layer of cubes will be placed. Waves will be lanced to stabilize this layer

before collocating the second layer of Cubipods. Afterwards the tests C2B and C1B with a

toe were executed. The toe berm is placed to sustain the bottom rows without making this

too rigid. To execute those two series of experiments (C2B and C1B), all the elements are

removed of the model, the toe berm is constructed, and the double layer of Cubipods is placed.

For the experiments with a single layer of Cubipods, the section C2B is removed and a new

layer with Cubipods is placed, and thus not the �rst layer of the former experiments, as done

in the tests without toe berm.

The two types of experiments without toe berm C2 and C1 are executed �rst because those

are the standard sections of the 'Ports of the State'. The models C2B and C1B with toe

berm however, are more realistic sections. In breaking conditions a lot of turbulence near the

bottom takes place, which can cause fast erosion of the lower part of the breakwater. Placing

a toe berm is therefore common.

The armour units in the model setup are painted in di�erent colours to easily recognize unit

movements during the experiments. The lower layer is completely white, while the upper layer

is painted in di�erently coloured strips. Also the cubes are painted in two di�erent colors:

white and blue.

5.4.2 Construction of the physical model

5.4.2.1 Preparation

First the wave �ume is cleaned and its interior is repainted with anti-oxidant paint.

The real cross section of the model breakwater is plotted and is attached to the inner side

of the wave �ume. Signi�cant points, indicated by a small gap, are marked correctly to the

�ume wall and the cross section can be drawn correctly (Fig 5.7). The cross section is also

painted at the other side of the wave �ume by perpendicular projection.

The �oor of the canal is cleaned and a concrete grout is poured in the wave �ume on the place

where the breakwater will come, which provides a rough surface for the model (Fig 5.8).


Figure 5.7: Draw the cross section of the mound breakwater on the wall of the canal

Figure 5.8: The concrete grout to provide a rough surface for the model


5.4.2.2 Control of the material characteristics

The received materials for the core and the �lter layer show a great dispersion of particle

size. Therefore we make a granulomatric separation of the received materials and compare

this with the theoretical values. The used terms D15, D50 and D85 are the corresponding

diameters of the sieves where respectively 15%, 50% or 85% of the materials can pass. Also

the Cubipods need to have the correct theoretical weight and density, to afterwards be able to

make right conclusions concerning the stability of those elements. For a part of the Cubipods

the practical values are measured and controlled with the theoretical ones.

The core (G2) The proposed particle size of the core material for the mound breakwater

is D50=7mm and D85/D15=2. After the sieving, the granulometric distribution is controlled

and the material is washed. The results can be seen in table 5.3 and in �gure 5.9. There can

be concluded that the theoretic and the real values di�er very little, which means that the

theoretic values are accepted.

The �lter layer (G1) The proposed particle size of the core material for the mound break-

water is D50=17mm and D85/D15=1.5. After sieving, the granulometric distribution is also

controlled and the materials of the �lter layer are also washed. The results can be seen in

table 5.4 and in �gure 5.10. There can be concluded that the theoretic and the real values of

the �lter material di�er very little, which means that the theoretic values are accepted.

The armour layer (G0) The Cubipod model units are fabricated by a private enterprise,

and are supposed to be delivered in the requested size and weight. To verify this, a part of the

Cubipods (5%) are weighted to know their real average weight and the standard deviation.

Obtaining the results in table 5.5 , the proposed theoretical values are considered satisfactory

and thus accepted.


theoretic design values measured values

Sample weight [g] 3000 3001,5

D85 [mm] 9,25 8,55

D50 [mm] 7,00 6,75

D15 [mm] 5,50 5,20

D85/D15 1,68 1,64

W85 [g] 2,14 1,69

W50 [g] 0,93 0,83

W15 [g] 0,45 0,38

Table 5.3: Grading characteristics of the core material

Figure 5.9: Grading curve for the core material


theoretic design values measured values

Sample weight [g] 3000 3001

D85 [mm] 21,00 20,59

D50 [mm] 17,50 17,82

D15 [mm] 14,00 15,24

D85/D15 1,50 1,35

W85 [g] 25,00 23,55

W50 [g] 14,00 15,27

W15 [g] 7,41 9,55

Table 5.4: Grading characteristics of the �lter material

Figure 5.10: Grading curve for the �lter material


weight [g] density [g/cm3] volume [cm3] D50 [cm]

Theoretical values 128 2,30 55,65 3,82

Measured average dry 128 2,29 55,86 3,823

Measured standard deviation dry 2,37 0,008

Measured average saturated 129,2 2,29 56,44 3,84

Measured standard deviation saturated 2,36 0,011

Percentage measured 5% 5%

Table 5.5: Theoretical and measured characteristics of the Cubipods

Figure 5.11: Construction of the model: the core and the �lter

5.4.2.3 Construction of the model

First, the core material is put in place according to the indicated lines on the �ume walls. A

perfect placement of the core is very important because it has to support the other layers: the

�lter and the armour layer. Afterwards, the �lter is constructed with a thickness of 6,67cm

only on the outer slope, making sure that the slope is constant over the whole width of the

breakwater. On the inner slope no �lter material is placed (Fig 5.11).

Finally the armour units are collocated. The theoretic thickness of the layer is the equivalent

cube size of the Cubipod, being 3,82cm. The number of collocated units depends on the

proposed theoretical porosity. In collocation tests with a crane, they have seen that the

porosity of Cubipods placed in a 'blind' way can vary between 36% and 50%. For this reason,


in those experiments will be worked with a proposed porosity of 41%, which is comparable to

earlier tests. The theoretic number of the units per area and per row to collocate to reach a

porosity of 41% can be calculated with the formulae 5.1 and 5.2, a number of 19 elements per

row is found. The way of collocating the units, however, is done randomly, as is also done in

real life. They let the elements fall without determining a certain position before. This means

that the number of elements sometimes can di�er from the theoretic calculated number. If

there was no place left for 19 elements, 18 units were collocated. In the reverse case, if there

was place left, an extra Cubipod was placed. This caused a little di�erence in porosity. In

table 5.6 can be seen that the initial porosities of each Cubipod strip are between 36% and

50% which are acceptable values. Only the porosity of the cube layer is lower than 36%.

Before placing the Cubipods, tests on the cube layer were executed and this provocated face

to face �tting of the cubes. Therefore the porosity of this layer is lower than 36%. Details of

this calculation can be seen in Appendix E.

Ntheor =(1− P )VtD50

3 (5.1)

number

row=

(1− P ) bD50

(5.2)

With

� P the porosity of the armour layer

� Vt the theoretic volume of the determined elements in m3

� D50 the size of the equivalent cube

� b the width of the canal being 1,22m

In �gure 5.12, the construction proses of the armour layer for a double layer of Cubipods C2

is shown step by step. First the under layer of white Cubipods is collocated, afterwards the

second layer with the di�erent colours covers this under layer. It is clear that the elements

are placed randomly and are not following an exact line, which is also in reality.


Color Preal C2 Preal C2B Preal C1B Preal CB

white 41 42 - 24

cyan 41 42 39 37

yellow 41 38 41 35

red 41 36 38 35

grey 41 42 39 35

blue 41 39 38 38

green 41 39 39 36

magenta 41 38 38 38

yellow 41 39 39 39

cyan 39 39 39 39

Table 5.6: The real initial porosity in the di�erent models [%]

For the other models C2B, C1B and CB, the way of construction is the same. For the

combined layer CB, �rst some waves are lanced to stabilize this cube layer, before collocating

the Cubipods. The single layer of Cubipods (C1) is formed by removing the second layer of

Cubipods of B2 and thus is formed by the same number of Cubipods as the �rst layer of C2.

5.4.2.4 Reconstruction of the model

After the �rst experiments however, the core and the �lter are destroyed partially. To guaran-

tee their stability, a change is executed in the construction of the core and �lter structure. As

the �lter was only constructed on the outer slope, now also a �lter layer is placed on the inner

slope to guarantee a higher stability. Further, on the top of the breakwater, a little crest with

�lter material is built on the inner side of the mound breakwater, to sustain the Cubipods

placed over there. This change can be seen in �gure 5.13 and in the sections in �gure 5.5

and 5.6. For the further experiments, this construction is always used, which means that the

experiments are not done with the real section of 'The ports of the State', but with a little

change to guarantee the stability in the following experiments.


Figure 5.12: Construction proses of the armour layer


Figure 5.13: Construction of the �lter on the inner slope and a crest on the top of the mound

breakwater after destruction of the core and the �lter layer

5.4.2.5 Placement of the sensors

The wave gauges are placed in the main line of the canal between the wave generator and

the breakwater model in two di�erent groups, one group of four wave gauges near the wave

generator and another group of four wave gauges near the model. Furthermore, a ninth wave

gauge is place on the breakwater model to measure the run-up. Those nine wave gauges will

permit us to obtain the incident and re�ected wave in the canal. The most important group

of wave gauges is the one near the model, the measured values will be used to calculate the

stability of the mound breakwater. The other group near the wavemaker is rather to know if

the wave generation is representative for those that really need to be generated.

The distance between the wave gauges of the same group are determined according to the

criteria proposed by Mansard and Funke, based on the used wave periods and lengths. They

propose three wave gauges per group and recommend the following distances, relative to the

used wave length:

� d1 ≈ L10

�L6 < d1 + d2 <

L3

� d1 + d2 = L5

� d1 + d2 6= 3L10


Position in the canal [cm] Wave gauge 1 Wave gauge 2 Wave gauge 3 Wave gauge 4

Near wave generator 340 360 410 440

Near model 1446 1476 1526 1546

Distance [cm] d1 d2 d3

Near wave generator 20 50 30

Near model 30 50 20

Table 5.7: Position of the wave gauges and distance between them in the canal

In the present experiments the four wave gauges in each group are separated according to

these recommendations. The eventually lack of one of the equations, however, is not a big

problem because we have four wave gauges in every group. Anyhow, the wave gauges are

placed in a way that all occurring waves and wave lengths can be registered accurately, and

the gauges can be kept �xed for all wave periods to avoid loss of time.

Another restriction to the positioning and separation of the gauges is that they should be

at least one meter away from the bottom slope in the centre of the �ume, to keep the gauge

registering away from being in�uenced by a change in water depth. This results in the dis-

tances between the wave gauges shown in Table 5.7.

5.4.3 Experiments

5.4.3.1 Realized experiments

To study the hydraulic stability of the Cubipod armour units, both, regular and irregular wave

tests are considered. However, in this project only the regular waves will be studied because,

before they experienced that irregular waves do not damage more than regular waves.

In regular wave tests, the wave in every experiment is characterized by his wave height and pe-

riod. The representative wave height is the average wave height (Hm). Increasing water depths

are considered (h=30cm, h=35 cm, h=38 cm, h=40 cm). For each of those water depths; a

series of increasing periods (T(s)=0.85s, T(s)=1.28s, T(s)=1.70s, T(s)=2.13s, T(s)=2.55s) is

considered, while for every period, a series waves with increasing design wave height (step of


1cm) is lanced.

Starting with wave heights that don't produce damage, the heights are increased until the

waves break (this is the maximum wave height compatible with the water depth) in the

model. In practice wave trains of 100 waves were executed.

5.4.3.2 Experimental procedure

Every day, before starting the experiments, �rst the water level is controlled. The loss of water

had to be compensated and during the tests, the depth was automatically and continuously

measured and compensated when necessary.

Having the correct water level, the manual calibration of the wave gauges can be done. This

is done by moving them up and down over a range of 15cm (10cm for the wave gauge on the

mound breakwater) while a second person adjusts the measurements in the data acquisition

system. After the calibration, a wave is lanced and the data registered by the wave gauges

is reviewed to make sure that all of the wave gauges continue to measure correctly. This is

done by opening the measured data in an Excel �le and plotting them. If one of the sensors

doesn't work correctly, calibration of this sensor has to be repeated.

Before starting the tests, a photograph of the armour layer is taken. One with and one without

the virtual framework, which is used to de�ne the nine strips that divide the slope for damage

analysis.

Every test set with a certain water depth, is started with a wave height that for sure will not

produce any damage to the armour layer. Before starting a new test, the water in the canal

has to be still, to make sure that all in�uence of earlier introduced waves was excluded and

could not in�uence.

During each test, the breakwater slope is guarded by a camera so the damage progression can

be looked after.

After every test, a photograph is taken with a �xed camera perpendicular to the slope. Those

are used afterwards to analyse the damage progression using the virtual net method.


After every test, the wave height is increased by one centimeter until breaking of the waves

occurs. Some (two or three) waves with higher wave height are lanced to be sure that the

maximum wave height will be reached. Then, waves with a higher period (and again a low

wave height) are lanced. After the complete test set of the �ve di�erent periods, the water

depth is changed.

The registered data by the wave gauges are �rst analysed by the software LASA-V. This

programme separates incident and re�ected wave trains. Afterwards those results are examined

by the software LPCLAB. This software generates a report that represents all the requested

and useful information about the waves.

The pictures made by the camera, are loaded in Photoshop to draw a virtual framework on

it. Afterwards this photograph is loaded in AutoCAD to indicate the Cubipod by points and

to calculate the damage progression using the Virtual Net Method.

5.4.4 Procedure to analyse the data

5.4.4.1 Separating the incident and re�ected waves: LASA V

The response of maritime structures depends on the incident wave �eld, however in laboratory

model tests as well as in prototype only the incident wave added to its re�ection can be

measured. This makes it necessary to distinguish the incident wave train seperated from the

re�ected wave train to study and predict response of maritime structures both in model tests

and in prototype.

Various methods for wave separation have been developed, a short resume can be found in

Appendix D. In this project, the separation of the waves is done using the LASA-V method,

proposed by Figueres and Medina [55]. This method is an optimization of the 'LASA local

wave model' method developed by Medina [54], based on linear and Stokes-II nonlinear com-

ponents and a simulated annealing algorithm to optimize the parameters of the wave model

in each small local time-segment of the measured record. To obtain the water surface eleva-

tion corresponding to the incident and re�ected wave trains at any point of the record, the

results of the optimization in each time window overlap. The optimized model that is used in


Figure 5.14: Parameter window of the LASA-V software

this Masterthesis uses an approximate Stokes-V wave model. This model is able to analyse

experiments with highly nonlinear waves, as in intermediate depth conditions.

The seven parameters controlling the simulated annealing process are: cost function, gener-

ation mechanism, initial solution, initial control parameter, reduction of control parameter,

length of markov chains and stop criterion. Those have to be implemented in the program,

also the number of linear wave components, number of nonlinear Stokes V wave components

and the duration of the time window which is �xed to 2∆t = 2T0 (Fig. 5.14). The program

LASA-V is applied to the four sensors near the model and near the slab. These results are

referred to the central sensors (here S3 and S7).

5.4.4.2 Analysis of the waves: LPCLAB 1.0.

After separating the incident and re�ected waves by LASA-V, the waves are analysed by a

sofware, developed by the laboratory of Ports and Coasts in Valencia, LPCLAB 1.0. This

software analyses the wave data in time- and frequency domain, generating a report in Excel


Figure 5.15: Example of the separation of incident and re�ected wave trains by LASA V

with all the relevant wave parameters, as well as some graphics. An example of such a report

is represented in Appendix ??.

In the beginning the register of the sensors is not regular due to transition. From the slab

without movement to movement you need time to generate the correct height. At the end, the

same phenomenon occurs, the slap can't stop immediately. To analyse the dates with LPCLab

1.0, we select the central part of the register, ignoring the transitions in the beginning and at

the end as shown in �gure 5.16.

The most important parameters for further research are the wave re�ection coe�cient, the

Iribarren number and the measured wave heights. We will use the average wave heights Hm and

H1/10 for further calculations. Those real wave characteristics di�er from the theoretic values,

depending on various parameters like the wave generation, propagation and re�ection. For a

correct analysis of the breakwater behaviour, it is critical that the real wave characteristics

are taken into account correctly.

There are four graphics generated. Two concerning the measurements near the slab, and

the two others concerning the measurements near the model. The �rst always shows the

measured wave together with the sum of the calculated separated waves. The second graphic

shows the calculated incident and re�ected waves separated. Further, there are two more

graphics showing the wave spectrum.


Figure 5.16: Parameter window of the LPCLab software

After utilizing the programs LASA-V and LPCLAB 1.0. we know the next wave heights:

� Htotal registered in the sensors: Ht

� Hre�ected by separating the wave: Hr

� Hincident by separating the wave: Hi

� Hregenerated, total by counting up the incident and the re�ected wave: Hrt

Hrt should �x with Ht to consider that the separation was done correctly.

5.4.4.3 Analysis of the re�ection coe�cient

The re�ection coe�cient is the ratio of the re�ected wave height to the incident wave height,

and is calculated by the program LPCLAB 1.0. This value indicates how much energy is

dissipated by the mound breakwater and how much energy is re�ected.


CR =Hr

Hi. (5.3)

The wave height used to establish this re�ection coe�cient is the average wave height in regular

wave tests (Hm). The re�ection coe�cient depends on the characteristics of the wave (wave

length, wave period, water depth) and on the type of construction. To show the in�uence

of those wave characteristics; the re�ection coe�cient will be described in function of two

di�erent values: the Iribarren number or the dimensionless relative water depth kh:

Ir =tan (α)√

HL0

(5.4)

kh = 2πd

L(5.5)

The re�ection coe�cient mainly depends on the wave length. Therefore, a good way to show

the results will be in function of the dimensionless relative water depth, knowing that this

parameter only shows the in�uence of the wave lengths.

The number of Iribarren shows the in�uence of both wave height en wave length, and thus

seems not ideal to represent the re�ection coe�cient results. The number of Iribarren however,

also called the breaker parameter, describes a certain type of wave breaking (Table 4.1). The

relative amount of wave energy that can be re�ected o� a slope depends intimately on the

breaking processes . Because of this, it is natural to try to relate the re�ection coe�cient to

Ir. The graphics showing the re�ection coe�cient in function of the Iribarren number will

give us information about the relation between the re�ection on the mound breakwater and

the type of wave breaking.

Both representations, the re�ection coe�cient in function of the dimensionless relative water

depth and in function of the number of Iribarren, will be accomplished for the executed tests.

5.4.4.4 Analysis of the damage progression

In all the executed tests, the damage progression of the breakwater armour layer was analysed

both quantitatively with the Virtual Net Method and qualitatively through visual analysis


of photos after each test. Important to mention is that this analysis is done after seperating

incident and re�ected wave, and thus calculating with only the incident wave height.

Quantitative analysis Conventional analysis of mound breakwater takes into account only

the armour unit extraction failure mode; therefore, traditional methods, as there is the visual

counting method considers only the extraction of armour units assuming constant porosity to

measure damage of the armour layer.

The visual counting method de�nes the eroded area by:

A =NeDn50

3

b (1− p)=NeDn50

3

bφ(5.6)

And the dimensionless damage by:

S =A

Dn502 (5.7)

In which Ne is the number of eroded armour units, Dn50 is the equivalent cube size or nominal

diameter, p and φ = 1 − p are the constant porosity and packing density coe�cient of the

armour layer and b is the observed cross section width.

When Heterogeneous Packing takes place, the porosity of the armour layer changes over time,

and the equivalent dimensionless armour damage should be measured taking into account the

changes in porosity for each area of the armour layer in regard to initial porosity. Gómez-

Martín and Medina (2006) described the Virtual Net Method to measure the equivalent di-

mensionless armour damage. This method involves projecting a virtual net over the armour

layer dividing it into nine strips, each of which is n times the width of the equivalent cube

Dn50 (Fig 5.17). The dimensionless damage in each strip can be calculated using the equation:

Di = n

(1− φi

φ0i

)= n

(1− 1− pi

1− p0

)(5.8)


In which p0 and φ0i are the initial porosity and packing density coe�cient, respectively. pi

and φi are the porosity and packing density coe�cient after the wave attack. Pi takes into

account the number of elements in every strip, using the following equation:

pi = 1− NiDn502

ab= 1− φi (5.9)

Ni is the number of armour units in strip i (upper layer), the dimensions of each strip are the

strip height 'a', being n times the equivalent cube size, and the strip width 'b', here 75cm.

Not the whole width of the mound breakwater is considered, but only the central part. The

extreme parts are not taken into account to avoid calculating with parts in�uenced by of the

�ume wall.

Counting up the armour damages in each strip over the slope, the equivalent damage De can

be obtained using the following equation:

De =∑

Di (5.10)

where only the damages higher than zero are taken into account. A damage higher than zero,

means loss of packing density (higher porosity). A negative value of the damage stands for

a higher packing density, which means higher stability and thus not considered as damage.

Only the positive values of the calculated damages in the di�erent strips are counted up to

receive the total damage.

The most important advantage is that this method takes into account the change of porosity

in the armour layer, caused by Heterogeneous Packing or unit extraction.

After every test, a photograph perpendicular on the mound breakwater is taken using a camera

that is placed on a standard over the wave �ume. Every photo corresponds with a certain

water depth, wave-height and period. A real metal net that can be placed on the top of the

armour layer is used to divide the armour layer in nine strips. Only the �rst and last photo

of the day could be taken with this real metal net, because of the presence of the Step Gauge

above the model during the tests. Therefore, an equal virtual net is drawn with the graphical


computer program 'Photoshop' on the photos without the real net. It's important that the

camera doesn't move, to make sure that this virtual net is placed equal as the real net (Fig

5.18).

Using the technical drawing program AutoCAD, every Cubipod is marked with a point, using

di�erent layers for the di�erent strips of the armour layer (Fig 5.17). With the command

PRICAPAXYZ, developed by LPC, the Cubipods in every layer can be counted easily. With

this result, the porosity of every strip and thus the damage can be calculated with the former

equations.

As we are interested in the behaviour of the mound breakwater after a series of waves, and not

after every wave, we calculate the dimensionless damage only after a series of tests. At the

end of a sequence of tests with a constant water depth (h=30cm, h=35cm, h=38cm, h=40cm,

h=42cm), the dimensionless damage will be measured.

Figure 5.17: Virtual net to measure the equivalent damage analysis and counting the units in Au-

toCAD for damage calculation


Figure 5.18: Above: foto with the real net and the designed net in Photoshop (start of the tests

with h=38).

Under: foto without the real net and the pasted virtual net in Photoshop (end of the

tests with h=38)


Qualitative analysis To verify qualitatively the failure modes, it's necessary to de�ne a

method to validate the level of damage. To de�ne this level, there are di�erent classi�cations:

Losada et al. (1986) [27] proposed the following three damage levels: Initiation of Damage

(IDa), Initiation of Iribarren Damage (IIDa), and Destruction (De). In order to me more

precise, another stage of damage is included by Vidal et al.(1991) [28] called Initiation of

Destruction (IDe). They are de�ned through a visual analysis of photos after every test.

Those four damage levels were de�ned based on experimental information and provide an

internationally known basis for comparison with other results. A representation of the four

damage levels is given in �gure 5.19.

Initiation of damage (Ida)

This level of damage de�nes the condition attained when a certain number of armour units

are displaced from their original position to a new one at a distance equal to or larger than a

unit length. Holes larger than average porous size are clearly appreciable. In this research we

adopted for this number a value of 2% of the displaced units required to achieve Iribarren's

damage.

Initiation of Iribarren damage (IIDa)

This damage occurs when the extension of the failure area on the main layer is so large that

the wave action may extract armor units placed on the lower armour layer.

Initiation of Destruction (IDe)

A small number of units, two or three, in the lower armour layer are forced out and the waves

work directly on pieces of the secondary layer.

Destruction (De)

Pieces of the secondary layer are removed. If the wave height does not change the mound will

de�nitely be destroyed and it will cease to give the level of service de�ned in the design.

The wave height corresponding to the three signi�cant damage levels (IDa, IIDa and IDe) is

obtained out of the visual qualitative analysis and in each case the corresponding dimensionless

armour damage will be calculated. The wave height corresponding to the initiation of damage

will be used to calculate a �rst estimation of the hydraulic stability factor KD.


Figure 5.19: Damage levels in the armour layer

Chapter 6

Results

6.1 Introduction

In this chapter, the results of the executed experiments are discussed and is subdivided in

three parts. In the �rst part the results of the �ume calibration are presented, which have

an important in�uence on the physical model tests. A good working of the wavemaker is

necessary to be able to interpret the obtained results afterwards. In the second part, the

discussed theories to calculate the maximum wave height in breaking conditions are compared

with the measured results in the laboratory. Further, in the last section, the results of the

experiments on the mound breakwater model of Cubipods are commented. Both results on

wave re�ection and on damage progression of the armour layer are presented. The damage

is studied qualitatively and quantitatively. A �rst indication of the value of the hydraulic

stability coe�cient is calculated for the di�erent mound breakwater sections in shallow water.

All the results of the di�erent studied sections �rst will be described, then explained and �nally

compared with the obtained results of the other sections. Graphics are used to illustrate the

results in a clear way. A comparison with earlier executed tests in deepwater conditions is

also done.

An overview of the executed tests and the most important results can be found in Appendix G,

while the complete results of the LPCLab test reports can be found on the available cd-rom.

A short explanation of the used terminology is resumed in Appendix A.

77

Results 78

6.2 Calibration of the wave �ume

As mentioned in Chapter 5, before starting the experiments, the calibration of the wavemaker

is executed. This calibration has been carried out with the following characteristics:

� The generated wave is irregular with a JONSWAP spectrum (γ = 3, 3)

� The considered water depths are 40cm, 45cm, 50cm and 55cm (near the wavemaker)

� Wave periods of 1s, 1,5s, 2s, 2,5s and 3s are used

� Wave heights between 2cm and 30cm are lanced

� The energy dissipation system that will be used during the model experiments has been

put in place

� The AWACS active energy absorption system in the wavemaker is put in place to guar-

antee a constant wave generation

� The measurement of the generated wave height is registered simultaneously, and is mea-

sured by a sampling frequency of 20Hz

To control the operation of wavemaker, the theoretical dates (wave height and wave period) of

the lanced wave are compared with the measured wave height and wave period in the sensor

near the wavemaker, being sensor 3. Those results are represented graphically in �gure 6.1.

We see that the real average wave height near the wavemaker is less than the theoretical value,

a di�erence that increases with increasing wave height and decreasing period. This di�erence

is due to the loss of energy in the wave �ume. This energy loss increases with increasing wave

height and decreasing period. Larger the wave height and smaller the period, larger the loss

of energy, and larger the di�erence between theoretical and measured value. In the graphic of

the period can be seen that the real period and the theoretical period correspond very well.

Concerning those graphics, we can decide that the wavemaker realizes the waves with the

asked characteristics.

Results 79

Figure 6.1: Results of the calibration of the wave �ume

Results 80

6.3 Interpretation of the theories calculating the maximum wave

height

The theoretical breaker height and breaker depth are presented in di�erent graphics using the

presented models in Chapter 4 to calculate the characteristics of breaking waves. Further,

those results are compared with the measured results in the laboratory.

The following characteristics are taken into account:

� As the tests are done with a horizontal bottom, the slope α in the executed tests is zero.

� The water depth in shallow water is the water depth near the model, being 25cm less

than the water depth near the wavemaker.

� The measured wave heights used to compare with the di�erent theories are the incident

wave heights (after separating the total heights by the software LASA-V). This means

that the in�uence of the present mound breakwater, being the in�uence of the re�ected

wave on the total wave height, is eliminated.

� As the breaking wave height Hb, the highest value of the maximum wave heights near

the model is taken.

� To calculate the wavelength L0 in deepwater, the Airy formula (1845) is used: L0 = gT 2

2π

� As measured wave height in deepwater H0, the measured wave height near the wavemaker

is used. This is not totally correct, because the the situation near the wavemaker is

in intermedias water depths. The measured wave lengths will not reach L0 and the

measured wave heights will be higher than H0.

The models proposed by Keulegan and Patterson, Collins, SPM and Demirbilek and Vincent

depend only of the breaking depth and the bottom slope. Those can be visualized in a graphic

showing the breaking wave height in function of the water depth. For the formula of Collins

and of SPM and Demirbilek and Vincent, three curves are drawn with three di�erent bottom

slopes: a horizontal bottom (as in the executed tests), a smooth slope of 3O and a steeper

slope of 10O (Fig 6.2).

Results 81

All the theories give a linear link between the two variables. As the water depth increases,

the breaking wave height also increases with a certain factor.

We see that the lower boundary of the theory of Keulegan and Patterson and the model of

Collins for horizontal slopes give us the smallest values of breaking height. Little higher values

are given by the upper boundary of Keulegan and Petterson together with the model of Weggel

for a horizontal slope. The values concerning the theory of Collins, change a lot in function

of the bottom slope. The highest wave on a water depth of 30cm is 21,6cm for a horizontal

bottom, while this is 30,40cm for a bottom slope of 3O and increases until 51,22cm if the slope

becomes 10O.

The model of SPM and Demirbilek and Vincent also shows the in�uence of the bottom slope,

but the in�uence of the slope is rather small. The highest wave that can exist in a water depth

of 30cm changes from 25,05cm to 25,18cm until 25,49cm when the bottom slope changes from

horizontal to 3O until 10O. This di�erence is very small. For a horizontal bottom the model

of SPM and Demirbilek and Vincent gives higher values than Collins, but for higher bottom

slopes, the values of Collins are clearly higher.

Comparing those results with the results measured during the experiments, we see that the

lower boundary of Keulegan and Patterson and the model of Collins (horizontal bottom)

estimates the breaking wave height very well. The upper boundary of Keulegan and Patterson

and the theory of Weggel overstimate the breaking wave height a bit, and SPM and Demirbilek

and Vincent give us an overly conservative estimation which can increase the cost of a project.

The lower measured breaking wave height for depth 40cm than for depth 38cm, is not possible,

and the reason has to be searched in the measurement system of the wave heights or the

analyses afterwards.

Concerning the formulae given by Komar and Gaughan and Sakai and Battjes, the relation

Hb/H0 can be described in function of H0/L0 (Fig 6.3). The values Hb, H0 and L0 of the

executed tests are de�ned as described above.

The two theoretical curves have the same form as the curve of the measured values. For

increasing H0/L0, which means decreasing wave period, the breaker wave height decreases.

For the same characteristics in deepwater conditions (means also for the same peiod), the

Results 82

Figure 6.2: Theoretical models to estimate the breaking wave height in function of the water depth,

compared with the maximum measured wave height: Keulegan and Patterson (K&P),

Collins for di�erent slopes, SPM for di�erent slopes and Weggel for a horizontal bottom

Results 83

Figure 6.3: Theoretical models to estimate the relation Hb/H0 in function of H0/L0, compared with

the measured results: Komar and Gaughan (K&G), Sakai and Battjes (S&B)

model of Sakai and Battjes gives higher values for Hb/H0 than the theory of Komar and

Gaughan. The measured values Hb/H0 however, are higher than both. This means that both

theories tends to underestimate the maximum wave height which could result in structural

failure or signi�cant maintenance costs.

The results of Le Roux are shown in a graphic giving the deepwater wave height H0, calculated

with the formula of Airy, in function of Hw, being the wave height in any water depth (Fig

6.4). To compare this theory with the measured results, we will �x a certain water depth,

being h=30cm. The same can be done for the other water depths. Concerning the iterative

method of Le Roux to calculate the characteristics, the breaker height is given by the formula

proposed by SPM concerning a horizontal bottom. This is in the graphics a horizontal line

given by: H = 0, 835 · 30cm = 25, 05cm, because we �x a water depth of 30cm.

Concerning the theory, we see that for increasing period, and a �xed deepwater wave height,

the real wave height increases. Also can be seen that the waves with a di�erent period have

the same breaking wave height, the wave height given by the formula of SPM and Demirbilek

Results 84

Figure 6.4: Theorecal model of Le Roux to estimate the real water wave height for h=30cm, com-

pared with the measured results

and Vincent, as explained in the theory of Le Roux. Ones reached the breaking wave height,

concerning Le Roux, all the waves with a higher deepwater wave height, will have an equal

maximum wave height in shallow waters. Comparing those results with the measured ones,

we see that for increasing period and a �xed deepwater wave height, the real wave height also

increases, however, we see also clearly that the measured results are a little higher than the

calculated values, which means that the real wave heights are underestimated by the theory of

Le Roux. Another di�erence is that the breaking wave height changes with the period, higher

the period, higher the breaking wave height. Further, we see that ones reached the maximum

wave height, for higher deepwater wave heights, the maximum wave height in shallow waters

decreases, it doesn't reach anymore the breaking wave height Hb. The reason therefore can

be found in the fact that how higher the deepwater wave height, how stronger the breaking

will be, saying that the loss of energy by breaking will be higher, which will result in a lower

wave height, as can be seen in the curves of the measured results. This fact, however is not

seen in the theoretical model of Le Roux.

Results 85

6.4 Hydraulic stability of the mound breakwater

6.4.1 Wave re�ection

As mentioned in 5.4.4.3, the re�ection coe�cient will be represented in function of the dimen-

sionless relative water depth �rst, and secondly in function of the number of Iribarren. Here

we don't make a di�erence between the models with or without toe berm, because this has no

in�uence on the re�ection coe�cient. The results in the di�erent sections are explained, and

further, the obtained results are compared with the results in deepwater conditions [36].

kh = 2πd

L(6.1)

Ir =tan (α)√

HL

(6.2)

6.4.1.1 The re�ection coe�cient in function of kh

In the three cases (double cubipod layer, single cubipod layer, and the combination of a cube

with a cubipod layer) the same tradition can be seen in the graphics showing the re�ection

coe�cient in function of kh (Fig 6.5).

First of all, we see that the executed tests can be divided in groups with a constant value

of dimensionless relative water depth. For a certain water depth and period, di�erent waves

with increasing wave height were lanced. This wave height, however, does not in�uence on

the wave length, so does not in�uence on kh. This means that the di�erent experiments with

the same water depth and the same period (but di�erent wave height) have a constant value

of kh, which explains the separated groups of points in the graphics.

Further can be seen that the wave length and wave period will play an important role. For

kh > 1, 5 the re�ection coe�cient is rather small, while for smaller kh values the re�ection

coe�cient increases, rising more steeply for kh approximately 0,50.

We conclude that there is a correlation between the wave re�ection and the parameter kh.

Small numbers of kh, and thus large wave lengths and small wave periods, coincide with higher

Results 86

re�ection coe�cients. The crest does not break on the slope but only runs up and down on

it. Few energy is being dissipated, which leaves room for signi�cant re�ection.

Double Cubipod layer - Single Cubipod layer Comparing the re�ection coe�cient in

case of two layers of Cubipods with a single layered mound breakwater, there can be easily

seen that for high values of kh, the re�ection coe�cient is clearly higher for a double layer of

Cubipods (15% - 25%) than for a single layer (7% - 15%). This di�erence however decreases

when kh decreases. For kh approximately one, the situation is opposite; the double layer

reaches values of 10% - 20% while the single layer reaches higher values from 15% to 25%.

For small values of kh the di�erence can be supposed as nil, for both sections, the CR varies

between 30% and 50%. (Fig 6.6).

Waves with small wave lengths will dissipate more energy on a one layered mound breakwater

than in case of a double layer. This di�erence for high values of kh is due to the higher porosity

in case of one armour layer, and thus easier access to the core to dissipate a lot of energy. Two

layers of armour elements decrease the access to the core and less energy will be dissipated,

thus a higher re�ection coe�cient will occur. Decreasing kh, however, means that the crest

does not break on the slope but runs up and down on it and the type of armour layer will

in�uence the re�ection coe�cient. A double armour layer can dissipate more energy than a

single one, which explains less re�ection in case of a double layered armour layer compared

with a single layer. Further increasing of the wave lengths, means less in�uence of the number

of armour layers on the re�ection coe�cient as can be seen in the graphics. The di�erence

in the coe�cient of re�ection is negligible for small kh, which means that a single layer of

Cubipods and a double layer of Cubipods dissipate the same energy in case of waves with high

wave lengths.

Double Cubipod layer - Combined layer A comparison of a mound breakwater consist-

ing of a cube-cubipod combined layer with a double layer of Cubipods is shown in �gure 6.7.

The results are very similar but for high values of kh, a double layered mound breakwater of

Cubipods re�ects a little less energy than in case of the combined cube-cubipod layer.

This is due to the fact that cube elements tend to re-organize its units to an almost solid

Results 87

plate where all the cubes have the same orientation and with a very low porosity. Therefore,

less energy can be dissipated and more re�ection occurs. As this cube layer is covered by a

cubipod layer, this re-organization will only take place partially, which means that the porosity

in the upper layer will be similar in both cases. This explains the little di�erence in re�ection

coe�cient between both.

Single Cubipod layer - Combined layer Also the comparison of a combined cube-

cubipod layer is made with a single cubipod layer (Fig 6.7). For high values of kh, the

re�ection coe�cient of the mound breakwater with one cubipod layer is less than in case of

the combined layer. Thus, for waves with small wave lengths, a mound breakwater with one

layer of Cubipods dissipates more energy than in case of the combined layer. Decreasing

the kh coe�cient, however, the re�ection coe�cient of the one layered cubipod armour layer

becomes a little higher then in the combined case.

The reason is the same as explained above in the comparison between the single and double

layer with only Cubipods. The higher porosity in case of one armour layer compared to two

armour layers, causes a lower re�ection of energy. As the double layered armour layer now also

has a cube layer, the di�erence is bigger, because those Cubipods tend to re-organize to an

almost solid plate with a very low porosity, which means that less energy can be dissipated. As

the wave length increases, the di�erence in re�ection coe�cient decreases and the importance

of the type of armour layer seems less important.

6.4.1.2 The re�ection coe�cient in function of Ir

The graphics showing the re�ection coe�cient in function of the number of Iribarren are also

enclosed (Fig 6.8). A clear di�erence can be seen between the re�ection coe�cient for waves

with Ir > 3 and Ir < 3. Small numbers of Iribarren coincide with little re�ection, while waves

with high numbers of Iribarren have a high re�ection coe�cient.

Experiments with small Iribarren numbers, where short wave lengths and thus small periods

occur, coincide with plunging breaking (0, 5 < Ir < 2, 5) and collapsing (2, 5 < Ir < 3). A lot

of energy is dissipated which means little re�ection.

Results 88

A high theoretical Iribarren's number, on the other hand, means large wave lengths and thus

large periods occur. High Iribarren numbers coincide with surging wave breaking. The crest

does not break on the slope but only runs up and down on it. Few energy is dissipated, which

leaves room for re�ection. This correlation between wave re�ection, number of Iribarren and

type of wave breaking is also shown in Battjes [8].

6.4.1.3 Comparing with the re�ection coe�cient in deepwater

Earlier tests were executed in deepwater on mound breakwaters with an armour layer existing

of a double layer of Cubipods. Those results can be compared with our tests. In deepwater

conditions, the re�ection coe�cient varies between 15% and 60%, and in shallow water between

10% and 50%.

As waves enter shallow water, their overall wave length shortens, the crest will break and thus

a lot of energy is dissipated which means little re�ection.

Results 89

Figure 6.5: The re�ection coe�cient (CR) in function of the dimensionless relative wave depth (kh)

Results 90

Figure 6.6: The re�ection coe�cient in function of the dimensionless relative water depth (kh):

comparing single and double layers of Cubipods

Results 91

Figure 6.7: The re�ection coe�cient in function of the dimensionless relative water depth (kh):

comparing a combined cube-cubipod layer with a double layer of Cubipods and a single

layer of Cubipods

Results 92

Figure 6.8: The re�ection coe�cient (CR) in function of the number of Iribarren

Results 93

6.4.2 Damage analysis on the armour layer

6.4.2.1 Introduction

To make a �rst estimation of the hydraulic stability coe�cient for the considered breakwater

sections in breaking conditions, damage analysis is executed using the qualitative method,

based on the photos made after every experiment. Further, to receive more exact results, the

damage progression is studied using a quantitative method, the Virtual Net Method described

by Gómez-Martín & Medina [24], taking into account the heterogeneous packing. A more

correct result is obtained. Here can be mentioned that during the experiments could be seen

clearly that heterogeneous packing took place before extraction of armour units.

6.4.2.2 Qualitative analysis

To make a �rst estimation of the hydraulic stability coe�cient, the damage is analysed quali-

tatively, using the photos made after every experiment. The aim is to obtain the value of the

incident wave height corresponding with Initiation of damage (IDa), Initiation of damage of

Iribarren (IIDa) and Initiation of destruction (IDe) using the de�nitions explained in 5.4.4.4

and to compare those results for the di�erent breakwater sections. Those values of incident

wave height will be used later on to estimate the hydraulic stability coe�cient, using the

Hudson [5] formula proposed by SPM[6]. As the tests were always stopped before IDe, only

the �rst two levels will be considered here. Concerning the de�nitions of the damage levels,

for a single layer of Cubipods, there is no di�erence between IDa and IIDa, thus only one level

is obtained. The results can be seen in 6.1.

The corresponding incident wave height producing those levels of damage, is taken as the

maximum of the signi�cant incident wave heights H1/10 of all the earlier lanced waves by this

type of armour layer.

The dimensionless damage corresponding to those two damage levels is calculated. They di�er

a little between the di�erent types of armour layers but the average values can be given as:

De=1,2 for IDa and De=3 for IIDa.

Results 94

IA IAI

De H1/10 [cm] De H1/10 [cm]

Double layer Cubipods without toe berm: C2 1,20 16,5 2,96 23,4

Single layer Cubipods without toe berm: C1 1,26 19,8

Double layer Cubipods with toe berm: C2B 1,32 19,7 2,97 23,6

Single layer Cubipods with toe berm: C1B 1,10 18,4

Combined layer: CB 1,37 16,9 3,15 23,6

Table 6.1: Incident wave heights producing the levels of damage: IDa and IIDa

For the double armour layer, the breakwater section with toe berm can resist a higher wave

height until IDa or IIDa occurs than in the situation without toe berm. The elements move

more downwards if there is no toe berm, thus damage will occur earlier.

For the single armour layer, the situation seems to be opposite. The reason therefore, however,

has nothing to do with the presence or absence of a toe berm. The executed tests on the section

without toe berm are formed by the �rst layer of B2, taking o� the coloured elements of the

upper layer. The elements of the under layer were already stabilized during the tests on the

double layered section and thus have a higher friction with the �lter, which means that they

can resist a higher wave height before reaching a damage level. The di�erence for the higher

wave height in case of a single layer B1 compared with the double layered breakwater B2, can

be explained in the same way.

The wave height corresponding with IDa for the double layered breakwater with toe berm

C2B is higher than for the single layered, which indicates a higher hydraulic stability of the

section C2B than of the section C1B.

For the combined section CB, no explicit conclusion can be made concerning the hydraulic

stability in comparison with the other sections. More tests are necessary to exclude the right

solution.

The formula of Hudson, proposed by SPM, to calculate the number of stability Ns is used to

Results 95

estimate the hydraulic stability coe�cient and is de�ned as:

NS =H1/10

∆Dn= (KDcotα)

13 (6.3)

KD =NS

3

cotα(6.4)

The incident wave height is de�ned as the signi�cant wave height H1/10 causing IDa, as

proposed by SPM [6]. Also here, the maximum signi�cant incident wave height of all the

earlier tests is taken as corresponding wave height. Knowing the breakwater slope (1:1,5), the

dimensions of the armour units (Dn=3,82cm for Cubipods and Dn=4,00cm for cubes), their

density (2,30t/m3) and the wave height producing IDa, the value of KD can be calculated. For

the combined layer CB, the calculation is done with the dimensions of the cubes, because this

results in a lower value of stability than when it should be calculated with the lower cubipod

dimensions.

KD=43 was found for double layer of Cubipods, KD=35 for a single layer of Cubipods and

KD=23 for a combined armour layer with cubes and Cubipods, knowing that this lower value

is also due to the calculation with the cube dimensions. Important to know is that those

values are valid for shallow water (breaking conditions), in the structure head of a mound

breakwater and random collocation of the Cubipods. Those values, however, are just a �rst

estimation. More experiments need to be carried out to optimize this parameter.

Important to mention is the high value of hydraulic stability coe�cient of Cubipods, compared

with other armour units. Some of them are published in SPM (1984) [6], those can be seen in

table ??.

Also necessary to mention is that the calculation of the hydraulic stability coe�cient here is

based on results of damage tests assuming damage by Heterogeneous Packing. Knowing that

this failure mode occurs almost always before extracting of armour units, the received results

here probably will be more exact than those received by the traditional methods.

Results 96

6.4.2.3 Quantitative analysis

The qualitative analysis gave us a �rst estimation of the stability of the di�erent armour

breakwaters. To obtain a more correct restult, however, a quantitative analysis is necessary.

The quantitative analysis of the damage is done using the Virtual Net Method, that compares

the porosity in every zone of the armour layer to the initial porosity and results in the equiv-

alent dimensionless damage, as explained in section 5.4.4.4. This can be transformed to the

linearized dimensionless damage by elevating it to the power 0,2 (Eq. 6.5). In a graphical

presentation this ultimate value provides a clearly understandable image.

D∗ = D0,2 (6.5)

After every series of tests with a constant water depth, the dimensionless damage De is calcu-

lated, and this for the di�erent studied models. Here, the same remark as in the qualitative

analysis about the wave height can be made. As corresponding wave height, the maximum

measured incident average wave height Hm during the series of tests with the concerned water

depth is taken.

If the linearized dimensionless damage D* values are represented simply as a function of the

corresponding scaled wave heights, it is rather di�cult to interpret them and to compare

them with other test results, especially because low density concrete is used. To provide a

more accurate representation and especially to be able to compare the obtained results with

the results of the earlier cubipod model tests in non-breaking conditions in deepwater [38],

the average incident wave height is divided by the wave height that causes IDa (HD=0) for

an equivalent cube with the density and weight of the used Cubipods, but KD of a regular

cube. Using the Hudson formula, this results in HD=0(KD=6)=10,03 cm. Thus, the linearized

dimensionless damage of the wave tests are presented with respect to a dimensionless wave

height: H1/10/HD=0,KD=6. With this conversion, the comparison with the former results can

be done e�ectively.

The results are also compared with the equation proposed by Medina et al. [47], based on the

test results for quarrystone in SPM [6]. Based on this equation, a general equation for each

type of armour unit can be deduced, where Hm is the average incident wave height:

Results 97

H1/10

HD=0=(D

1, 6

)0,2

(6.6)

D∗ = D0,2 = 1, 60,2

(4KD

)1/3 Hm

HD=0(6.7)

First, we study the in�uence of the presence of a toe berm by comparing both: the double ar-

mour layer with and without toe berm and the single armour layer with and without toe berm.

In the graphics (Fig 6.9) showing the results of the double armour layer is it clear that the

hydraulic stability is lower if there is no toe berm. After a series of experiments however can

be seen that this di�erence becomes nil.

In case of a toe berm the armour elements at the bottom of the mound breakwater can't

remove, and thus increase of porosity will only occur at the top of the breakwater. For the

elements near the bottom, the porosity decreases because the elements from above push them

down. When this toe berm is not present, however, the elements near the bottom can remove

and also here the porosity will increase, thus higher damage occurs in the beginning. After a

series of experiments, the removed elements are collected at the bottom and form a massive

entity, working like a toe berm, which explains the small di�erence at the end.

The graphics showing the results of the single armour layer, however, show the opposite.

The mound breakwater without toe berm seems to have a higher hydraulic stability. The

reason therefore, however, has nothing to do with the presence or absence of a toe berm. The

executed tests on the section without toe berm is formed by the �rst layer of B2, taking o�

the elements of the upper layer. The elements were already stabilized during the tests on the

double layered section and thus have a higher friction with the �lter layer. In the results of

the section without toe berm can be seen that at the top of the breakwater, little damage

takes place, the majority of the damage is due to the layers at the bottom, and thus due to the

absence of a toe berm. In the experiments with toe berm, there is no damage at the bottom

near the toe berm, but the damage is only due to removing units at the top of the breakwater.

In this case, an explicit conclusion can't be made.

Results 98

As mound breakwaters with toe berm are the common built breakwaters in breaking condi-

tions, the further hydraulic stability analysis will only be executed with this types of break-

water.

The graphics with the calculated dimensionless damage results (the isolated points in Fig 6.10)

show a di�erence between the three breakwater sections. The double layer gives more stable

results than the single layer of Cubipods, while the combined layer of cubes and Cubipods

gives the lowest results.

Changing KD by a certain hydraulic stability coe�cient in the equation 6.7, the equivalent line

for every armour unit can be drawn in the graphic showing D* in function of Hm/HD=0. We

can draw the lines with KD=43, KD=35 and KD=23, corresponding with the double Cubipod

layer, the single Cubipod layer and the combined layer of Cubipods and cubes, in the graphics.

Also the lines indicating IDa and IIDa are drawn. The result can be seen above in the �gure

6.10.

For the di�erent breakwater sections, the results of the dimensionless damage (the isolated

points) seem to be higher than the equations, using the qualitative calculated stability coef-

�cient predict, which means that the qualitative manner to calculate KD overestimates the

stability coe�cient. Better adjustment would be obtained with the line KD=28 for double

layer of Cubipods, KD=23 for a single layer of Cubipods and KD=18 for the combined layer

as we prefer to place the line on the safe side. This is shown in the second graphic of �gure

6.10.

Further, comparing the results with the executed tests in deepwater for a double layered

breakwater, there can be seen that the results in breaking conditions are less stable than in

non-breaking conditions. For the same incident wave height a higher dimensionless damage

is occurred in case of breaking conditions than in case of a non-breaking situation. On the

other hand, to receive a certain level of dimensionless damage, in non-breaking conditions a

higher incident wave height is needed than in breaking conditions. This is normal because in

breaking conditions, waves with higher energy reach the breakwater, which means that the

damage will initiate earlier than in deepwater conditions.

Results 99

Figure 6.9: In�uence of the presence of a toe berm on the hydraulic stability of a mound breakwater

Results 100

Figure 6.10: The linearised dimensionless damage as a function of a dimensionless height. Above:

the qualitative calculated KD's. Under: the quantitative calculated KD

Results 101

Figure 6.11: Comparison a double Cubipod layer in breaking with non-breaking conditions, and with

Quarrystone in breaking conditions. Dimensionless damage as a function of dimension-

less wave height

Chapter 7

Conclusions

The stability of the armour layer of a mound breakwater depends on many factors, but in

this project only the hydraulic stability of the armour units is studied, more speci�cally the

loss of armour elements in certain zones of the breakwater slope which can be caused by two

reasons: simple extraction of the armour units under wave attack or their excessive settlement

causing Heterogeneous Packing. The hydraulic stability in breaking conditions of the recently

invented Cubipod is studied.

The goal of the Cubipod unit is to bene�t from the advantages of the traditional cube, but

to correct the drawbacks. Therefore, the design of the unit is based on the cube in order to

obtain his robustness. The protuberances of the Cubipod avoid face-to-face settlement and

increase the friction with the �lter layer. They avoid sliding of the armour elements. Due

to this, Heterogeneous Packing and loss of elements above the still water level is reduced.

All this indicates a higher hydraulic stability of Cubipods in comparison with cube elements.

Furthermore, easy casting, e�cient storage and handling are other advantages.

As the incident wave height is an important factor in�uencing the design of coastal structures,

a short study is done concerning the maximum wave height in breaking conditions. Di�erent

existing theories were commented and compared with the measured values. In general can be

concluded that the theories overestimate the maximum wave height. Further, many theories

suppose that the energy from the broken waves is concentrated in the breaking wave height,

102

Conclusions 103

which meant that all the broken waves would have the breaking wave height in the sur�ng

zone. This statement however doesn't correspond with the measured results. The energy from

the broken waves is distributed back over the smaller wave heights in the distribution.

The aim of this �nal project was the experimental study of the behaviour of Cubipod breakwa-

ters under wave attack in breaking conditions. The most important results were the re�ection

coe�cient and the hydraulic stability coe�cient of the armour layer. The obtained results

were compared to the similar previous tests on Cubipod breakwaters in deepwater condi-

tions. The re�ection coe�cient of the Cubipod armour layer di�ers between 10% and 30% for

kh > 1, 5 and increases until 50% for small kh values. For high kh values, the type of armour

layer has a big in�uence on the re�ection coe�cient. For small values of kh, however this

in�uence decreases and becomes nil. Re�ections coe�cients in shallow water is lower than in

deepwater conditions because the crest breaks and a lot of energy is dissipated which means

less re�ection.

All tests proved that the Cubipod has a high hydraulic stability in breaking conditions, com-

pared with all other published armour unit values. Stability factors of KD=28 and KD=23

were obtained for respectively a double layer and a single layer of Cubipods. For a combined

layer with Cubipods above cubes, a stability factor KD=18 was obtained. Comparison be-

tween the damage progression in deepwater conditions and in shallow water shows us that

the hydraulic stability coe�cient in shallow water is less than in deepwater conditions. Waves

with higher energy reach the breakwater, which means that the damage will initiate earlier

than in deepwater conditions.

Finally, the Cubipod shows to be a very promising armour unit, with a simple and robust

shape, an easy placement pattern and a high hydraulic stability, also in breaking conditions.

It can certainly be a very good alternative for regular cubes, and when more experiments will

be carried out, probably as well for many other armour units.

Appendix A

Terminology of the experiments

Every experiment has a code: VBWX_YZAC, e.g. VB01_3216 or VB04_5117. The termi-

nology of the experiments is the following:

� The �rst two letters VB stand for the laboratory where the tests have been carried

out (V=Polytechnic University of Valencia) and for the conditions of the executed tests

(tests in breaking conditions).

� The next number (W) refers to the wave type. As we only consider regular waves, is

this number always 0.

� Further, the type of armour layer is de�ned by the following de�nitions:

� 1: double armour layer

� 2: single armour layer

� 3: double armour layer with toe berm

� 4: single armour layer with toe berm

� 5: cubipods above cubes

� The number 'Y' stands for the water depth in the model. The following values are

considered:

� 1: hmodel = 20 cm

104

Terminology of the experiments 105







� The next value represents the period of the lanced wave in model being:

� 1: T = 0.85 s

� 2: T = 1.28 s

� 3: T = 1.70 s

� 4: T = 2.13 s

� 5: T = 2.55 s

� The last two numbers describe the wave height in model. A wave height of 6 cm in

model, results in 'AC'=06, a wave height of 12 cm in model results in 'AC'=12.

Appendix B

Wave �ume

A detailed plot of the total test setup within the wave �ume is shown on the next page. From

left to right one can see: the wavemaker, a �rst group of four wave gauges, the transition slope,

the second group of wave gauges, the breakwater model, an extra wave gauge to measure the

run-up together with the Step-Gauge system and �nally in the right end the energy dissipator.

106

Wave �ume 107

Figure B.1: Cross section of the 2D wave-�ume of the Laboratory of Ports and Coasts of the Po-

litecnic University of Valencia

Appendix C

Working of the AWACS

Many authors and laboratories resolved the re-re�ection problem by placing an active re�ection

absorption system in the wave generator. Schä�er and Klopman (2000) [48] review various

types of those techniques. However, most of the wave absorption methods have not been

published and some doubts still remain regarding the true e�ectiveness of methods based on

sophisticated �lters and black boxes. The wavegenerator in the laboratory is provided with

an Active Wave Absorption Control System AWACS. A more detailed scheme of the working

of the AWACS, provided by DHI AWACS2, is given in �gure C.1.

Before starting any other software, the next steps in the central control unit behind the

wavemaker, have to be followed. First, the principal button, feeding the other two, has to be

swithed on. Than, the second button, providing 24V has to be swithed on, and last, the third

button that provides 220V. Now the control unit receives alimentation.

Afterwards the converter is activated to change analogical signals from the computer in optical

signals going to the control system of the AWACS. Then the software 'DHI Wave Synthesizer'

can be started (Fig C.3). Here, an important option is 'Active Absorption'. The AWACS only

will work if this option is activated, if not, the wavemaker will not take into account possible

re-re�ections.

Every day before starting the experiments, the two wave gauges should be calibrated. DHI

AWACS2 features self-calibration of the paddle-mounted wave gauges. This is done by putting

108

Working of the AWACS 109

the button DSC in the starting window of the program. First 'o�set scan' is done, this

comment is used to put the present water level of the wavemaker on zero. The number of

columns depends on the number of wave gauges, in our case two (called A & B). The standard

deviation in calm water is supposed to be more or les 0,002V. If the values of the standard

deviations are less than 0,005V, it is accepted. If not, the button 'skipp all' is pushed and the

o�set scan is executed a second time.

Afterwards the calibration is done. The program starts to work and the information on the

screen is actualizing continual. At the end, the old and new values have to be controlled and

should be similar.

Now the waves to generate can be de�ned. In the window 'wave parameter' we de�ne 'regular

waves' and further 'Stokes 1st order'. In this window the wave height in meters, the period in

seconds and the water depth in meters have to be introduced. All those values are in prototype

and without taking into account any scale.

In the next window 'wave generation' (Fig C.4), the scale of the used model has to be de�ned,

and should be higher than 1. The duration of the test is obtained by multiplying the theoretical

period of the experiment by the number of desired waves. The program calculates the amplitud

and the velocity of the wavemaker. It's important to check if the utilization of the wavemaker

is less than 100%.

Before putting the start button, the software 'Multicard' for the aquisition of the datas has

to be activated (Fig C.5). Here the water depth near the wavemaker has to be given, and in

the window 'toma los datos' the duration of the test has to be de�ned. This duration will be

little higher than the duration given in 'DHI Synthesizer' to be able to also have datas after

the wavegenerator stopped moving. After putting 'realizar ensayo' the wave height in cm and

the period in seconds of the model are asked.

Now the experiment can be started. When �nished, the datas has to be saved and the next

experiment can be started.


Figure C.1: A detailed scheme of the working of the AWACS

Figure C.2: The steps to activate the control system


Figure C.3: Software to manage the AWACS. Above: the startscreen

Under: the calibration of the AWACS


Figure C.4: Windows to realize the wave generation

Figure C.5: The program Multicard, for the aquisition of the datas

Appendix D

Seperation of incident and re�ected

waves

The response of maritime structures depends on the incident wave �eld, however in laboratory

model tests as well as in prototype only the incident wave added to its re�ection can be

measured. This makes it necessary to distinguish the incident wave train seperated from the

re�ected wave train to study and predict response of maritime structures both in model tests

and in prototype.

Various methods for wave separation have been developed but those, however can only separate

the incident wave from its direct re�ection on the breakwater, which means that they don't take

into account multire�ections in the wave �ume. Therefore, the wave �ume in the laboratory

is provided with an AWACS.

The basic method on which most existing techniques for separating incident and re�ected

waves in laboratory are founded is the two-point method. This method is popularized by

Goda and Suzuki (1976) [49] and is based on linear dispersion and wave superposition. This

method, however is only usefull in numerical and noise free simulations, but not when using

real measurements in wave �umes.

Some methods like the three-point least squares method of Mansard and Funke (1981) [50]

may reduce the instability and sensitivity to noise, but stationarity and linearity still remain

113

Seperation of incident and re�ected waves 114

as two fundamental principles of the frequency-domain techniques used by most laboratories

for separating incident and re�ected waves.

One of their main disadvantages is the inconsistency produced by the fact that future measured

data are needed to estimate earlier analysed data. Time-domain methods like those proposed

by Kimura (1985) [51] and further developed by Frigaard and Brorsen (1994) [52] or Schä�er

and Hyllested (1999) [53] resolve this problem but still assume linear models.

The LASA method (Local Approximation using Simulated Annealing) developed by Medina

[54] for the analysis of incident and re�ected waves in the time-domain, is based on a local

approximation model considering linear and Stokes-II nonlinear components, and a simulated

annealing algorithm to optimize the parameters of the wave model in each small local time-

segment of the measured record. To obtain the water surface elevation corresponding to the

incident and re�ected wave trains at any point of the record, the results of the optimization in

each time window overlap. The method can be used for nonstationary and nonlinear waves.

The LASA method has been compared with the 2-point method from Goda and Suzuki and

the method developed by Kimura and resulted very robust in numeric experiments and very

consistent in physical experiments with both regular and irregular waves. The method can

directly be applied to regular and irregular two-dimensional waves without excessive steepness,

using whatever number of measuring gauges. This implies a huge advantage for the use in both

prototype and laboratory model tests with irregular and nonstationary waves, considering the

fact that up till this time, no other methods were available to analyse adequately the wave

separation of this very common and necessary experiment type.

Figueres and Medina [55] optimized the 'LASA local wave model' method, based on linear and

Stokes-II nonlinear components to the 'LASA-V wave model' using an approximate Stokes-V

wave model. This model is able to analyse experiments with highly nonlinear waves as in

intermediate depth conditions.

Appendix E

Calculation of the initial porosity

Figure E.1: Calculation of the initial porosity

115

Appendix F

Example of a test report

An example of the report �le for the results near the wavemaker generated by the software

tool LPCLab is presented here. The reports of all the executed tests can be found on the

included cd-rom.

116

Example of a test report 117

Figure F.1: Example of a test report

Example of a test report 118

Figure F.2: Example of a test report

Appendix G

Test results

An overview of the executed tests and the most important results are given. The used ter-

minology of the experiments can be found in Appendix A and all the complete LPCLab test

reports can be found on the available cd-rom.

119

Test results 120

Test results 121

Test results 122

Test results 123

Test results 124

Test results 125

Test results 126

Test results 127

Test results 128

Test results 129

Bibliography

[1] Y. Goda. Random seas and design of maritime structures. University of Tokyo, 2000.

[2] V. Negro and O. Varela. Diseño de diques rompeolas. Colegio de ingenieros de caminos,

canales y puertos, 2002.

[3] M. Muttray, B. Reedijk, and M. Klabbers. Development of an innovative breakwater

armour unit. Delta Marine Consultance b.v., Gouda, The Netherlands, 2004.

[4] R. Iribarren. Una formula para el calculo de los diques de escollera. M. Bermejillo

Usabiaga, Pasajes, 1938.

[5] R. Iribarren and C. Nogales. Generalización de la fórmula para el cálculo de los diques de

escollera y comprobación de sus coe�cientes. Revista de Obras Públicas. Madrid., pages

239�277, 1950.

[6] J. Larras. L'equilibre sous-marin d'un massif de materiaux soumis a la houle. Le Génie

Civil, Septembre, 1952.

[7] Hudson. Laboratory investigation of rubble mound breakwaters. Journal of Waterway,

Port, Coastal and Ocean Division, 85(3):93�121, 1959.

[8] Shore Protection Manual U.S. Department of the Navy Waterways Experiment Station,

volume 2. Government Printing O�ce, Washington, 4 edition, 1984.

[9] T. Carstens, A. Torum, and A. Traetteberg. The stability of rubble mound breakwaters

against irregular waves. Proceedings of 10th conference on Coastal Engineering, Tokyo,

pages 958�971, 1966.

130

Bibliography 131

[10] J. Battjes. Surf similarity. Proceedings of 14th International Conferenc on Coastal Engi-

neering, ASCE, pages 466�479, 1974.

[11] PIANC. Final report of the international comission for the study of waves. annexe bul 1.

no. 25. 3, 1976.

[12] A.R. Whillock and W.A. Price. Armour blocks as slope protection. Proceedings 15th

conference on Coastal Engineering, Honolulú, pages 2564�2571, 1976.

[13] O.S. Magoon and W.F. Baird. Breakage of breakwater armour units. Symp design rubble

mound breakwaters, British overcraft corporation. Isle of Wight. Paper No. 6, 1977.

[14] M.A. Losada and L.A. Giménez-Curto. The joint in�uence of the wave height and period

on the stability of rubble mound breakwaters in relation to iribarren's number. Journal

of Coastal Engineering, 3:77�96, 1979a.

[15] M.A. Losasa and L.A. Giménez-Curto. An approximation to the failure probability of

maritime structures under sea state. Coastal Engineering, 5:147�157, 1981.

[16] M.A. Losada and L.A. Giménez-Curto. Mound breakwaters under oblique wave attack;

a working hypothesis. Coastal Engineering, 6:83�92, 1982.

[17] J.M. Desiré. Comportamiento de un Sistema granular bajo �ujos oscilatorios. Aplicación

a diques rompeolas de bloques paralelepipédicos. PhD thesis, Universidad de Cantabria,

1985.

[18] J.W. Van der Meer. Deterministic and probabilistic design of breakwater armor layer.

Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 114(1):66�80, 1988.

[19] C. Vidal, M. Losada, and E. Mansard. Suitable wave-height parameter for characterizing

breakwater stability. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE,

121(2):88�97, 1995.

[20] J.R. Medina. Wave climate simulation and breakwater stability. Proceedings of 25th

International Conferenc on Coastal Engineering, ASCE, pages 1789�1802, 1996.

Bibliography 132

[21] J.A. Melby and N. Kobayashi. Progression and variability of damage on rubble mound

breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE,

124(6):286�294, 1998.

[22] A. Vandenbosch et al. In�uence of the density of placement on the stability of ar-

mour layers on breakwaters. Proceedings of the Coastal Engineering Conference, ASCE,

124(6):1537�1549, 2002.

[23] J. De Rouck et al. Full scale wave overtopping measurements. Coastal Structures, pages

494�506, 2003.

[24] C. Vidal et al. Wave height and period parameters for damage description on rubble-

mound breakwaters. Proceedings of 29th International Conferenc on Coastal Engineering,

ASCE, pages 3688�3700, 2004.

[25] M.E. Gómez-Martín and J.R. Medina. Wave-to-wave exponential estimation of armour

damage progression. Proceedings of 29th International Conferenc on Coastal Engineering,

ASCE, pages 3592�3604, 2004.

[26] M.E. Gómez-Martín and J.R. Medina. Análisis de averías de diques en talud con manto

principal formado por bloques de hormigón. VIII Jornadas Españolas de Ingeniería de

Costas y Puertos, 2005.

[27] P. Bruun. Common reasons for damage or breakdown of mound breakwaters. Coastal

Engineering, 2:261�273, 1979.

[28] M.E. Gómez-Martín. Estudio experimental de la variabilidad y evolución de la avería

en el manto principal de diques en talud. Master's thesis, Universidad Politecnica de

Valencia, 2002.

[29] M.A. Losada, J.M. Desire, and L.M. Alejo. Stability of blocks as breakwater armor units.

Journal of Structural Engineering, ASCE, 112(11):2392�2401, 1986.

[30] C. Vidal, M.A. Losada, and J.R. Medina. Stability of mound breakwater's head and

trunk. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 117(6):570�

587, 1991.

Bibliography 133

[31] J. Van de Kreeke. Damage function of rubble-mounds breakwaters. Journal of Waterway,

Port, Coastal and Ocean Division, 95(3):345�354, 1969.

[32] Y. Oullet. Considerations on factors in breaking model test. Proceedings of 13th Inter-

national Conferenc on Coastal Engineering, ASCE, pages 1809�1825, 1972.

[33] R. Iribarren. Fórmula para el cálculo de los diques de escolleras naturales o arti�ciales.

XXI Congreso Internacional de la Navegación, Stockholm, 1965.

[34] A. Paape and H. Ligteringen. Model investigations as a tool part of the design of rubble-

mound breakwaters. International Seminar on Criteria for Design and Construction of

Breakwaters, Santander., 1980.

[35] D.D. Treadwell and O.D. Magoon. Reinforced concrete armor units for coastal structures.

Proceedings of 30th International Conferenc on Coastal Engineering, ASCE, pages 5175�

5183, 2006.

[36] P. Bakker et al. Development of concrete breakwater armour units. 1st Coastal, Es-

tuary, and O�shore Engineering Specialty Conference of the Canadian Society for Civil

Engineering, 2003.

[37] L. Mijlemans. Analysis of the stability of the armour unit cubipod in breakwater struc-

tures. Master's thesis, Universidad Politécnica de Valencia - Universiteit Gent, 2006.

[38] A. Corredor et al. Cubípodo: ensayos de estabilidad hidráulica 2d y 3d, estudio del

remonte y rebase, diseño del encofrado y ensayos de caída de prototipos. III Congreso

Nacional de la Asociación Técnica de Puertos y Costas, 2008.

[39] M.E. Gómez-Martín and J.R. Medina. Cubipod concrete armour unit and heterogeneous

packing. Proceedings of Coastal Structures, ASCE, 2007.

[40] A. Corredor et al. Casting system and drop tests of the cubipods armor unit. Mediter-

ranean Days of Coastal and Port Engineering, Palermo, PIANC Italy, 2008.

[41] J.A. Battjes and H.W. Groenendijk. Wave height distribution on shallow foreshores.

Coastal Engineering, 40:161�182, 2000.

Bibliography 134

[42] G.H. Keulegan and G.W. Patterson. Mathematical theory of irrotational translation

waves. Res. J. Natl. Bur. Stand., 24:47�101, 1940.

[43] L.A. Collins. Probability of breaking wave characteristics. Proceedings of the 12th Con-

ference of Coastal Engineering, ASCE, pages 399�414, 1970.

[44] J.R. Weggel. Maximum breaker height. Journal of Waterways, Harbors and Coastal

Engineering Division, 98:529�548, 1972.

[45] P.D. Komar and M.K. Gaughan. Airy wave theories and breakder height prediction.

Proceeding of 13th Coastal Engineering Conference, ASCEM, pages 405�418, 1973.

[46] T. Sakai and J.A. Battjes. Wave theory calculated from cokelet's theory. Coastal Engi-

neering, 4:65,84, 1980.

[47] J.P. Le Roux. An extension of the airy theory for linear waves into shallow water. Coastal

Engineering, 55:295�301, 2008.

[48] M. Figueres and J.R. Medina. Estimating incident and re�ected waves using a fully non-

linear wave model. Proceedings of 29th International Conferenc on Coastal Engineering,

ASCE, pages 594�603, 2004.

[49] J.R. Medina. Estimation of incident and re�ected waves using simulated annealing. Jour-

nal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 127(4):213�221, 2000.

[50] J.R. Medina, R.T. Hudspeth, and C. Fasardi. Breakwater armor damage due to wave

groups. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, 120(2):179�

198, 1994.

[51] A. Hemming, Schä�er, and G. Klopman. Review of multidirectional active wave ab-

sorption methods. Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE,

126(2):88�97, 2000.

[52] Y. Goda and Y. Suzuki. Estimation of incident and re�ected waves in random wave

experiments. Proceedings of 15th International Conferenc on Coastal Engineering, ASCE,

pages 828�845, 1976.

Bibliography 135

[53] R. Mansard and E. Funke. The measurent for incident and re�ected spectra using a least

squares method. Proceedings of 17th International Conferenc on Coastal Engineering,

ASCE, pages 154�172, 1980.

[54] A. Kimura. The decomposition of incident and re�ected random wave envelopes. Coastal

Engineering in Japan, 28:59�69, 1985.

[55] P. Frigaard and M. Brorsen. A time-domain method for separating incident and re�ected

irregular waves. Proceedings of 24th International Conferenc on Coastal Engineering,

ASCE, pages 202�203, 1994.

[56] H.A. Schä�er and P. Hyllested. Re�ection analysis using an active wave absorption control

system. Coastal Structures, pages 93�99, 1999.

hydraulic stability of cubipod armour units in breaking conditions

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